1 Simulación Proceso Espacio Temporal
1.1 Funciones
##Funciones de covarianza espacio temporal
exp_esp_temp=function(h,u,p){((p[1])^2)*exp(-h/p[2]-u/p[3])}
gauss_esp_temp=function(h,u,p){(p[1]^2)*exp(-(h/p[2])^2-(u/p[3])^2)}
cressie1=function(h,u,p){(p[1]^2/((p[2]^2*u^2+1)))*exp(-(p[3]^2*h^2)/(p[2]^2*u^2+1))}
Gneiting1=function(h,u,p){p[1]^2/((p[2]*u^(2*p[3])+1)^(p[4]))*exp(-(p[6]*h^(2*p[5]))/((p[2]*u^(2*p[3])+1)^(p[4]*p[5])))}
#Gneiting2=function(h,u,sigma,p){p[1]^2/((2^(p[3]-1))*p[7](p[3])*(p[2]*u^(2*p[3])+1)^(p[4]+p[5]))*(((p[6]*h)/((p[2]*u^(2*[3])+1)^(p[5]/2)))^p[3])*besselK(((p[6]*h)/((p[2]*u^(2*[3])+1)^(p[5]/2))),p[3])}
Iaco_Cesare=function(h,u,a,b,c){(1+h^p[1]+u^p[2])^(-p[3])}#separables mas comunes: gaussiano y exponencial p=(sigma,a,b)
Gaussiano=function(p,h,u){p[1]^2*exp(-p[2]^2*u^2-p[3]^2*h^2)}
Exponencial=function(p,h,u){p[1]^2*exp(-p[2]^2*u-p[3]^2*h)}#C R E S S I E - H U A N G (1999)
#sigma:desviacion estandar, a es el par?metros de escala del tiempo, b es el par?metros de escala del espacio, d es la dimensi?n espacial; a,b positivos
CH_1=function(h,u,p,d){(p[1]^2/((p[2]^2*u^2+1)^(d/2)))*exp(-(p[3]^2*h^2)/(p[2]^2*u^2+1))}
CH_2=function(h,u,p,d){(p[1]^2/((p[2]*abs(u)+1)^(d/2)))*exp(-(p[3]^2*h^2)/(p[2]*abs(u)+1))}
CH_3=function(h,u,p,d){p[1]^2*((p[2]^2)*(u^2)+1)/(((p[2]^2)*(u^2)+1)^2+(p[3]^2)*h^2)^((d+1)/2)}
CH_4=function(h,u,p,d){p[1]^2*(p[2]*abs(u)+1)/((p[2]*abs(u)+1)^2+(p[3]^2)*h^2)^((d+1)/2)}#el caso mas general de C R E S S I E - H U A N G (1999) es cuando d=2, entonces queda
CH_1=function(h,u,p){(p[1]^2/((p[2]^2*u^2+1)))*exp(-(p[3]^2*h^2)/(p[2]^2*u^2+1))}
CH_2=function(h,u,p){(p[1]^2/((p[2]*abs(u)+1)))*exp(-(p[3]^2*h^2)/(p[2]*abs(u)+1))}
CH_3=function(h,u,p){p[1]^2*((p[2]^2)*(u^2)+1)/(((p[2]^2)*(u^2)+1)^2+(p[3]^2)*h^2)^((3)/2)}
CH_4=function(h,u,p){p[1]^2*(p[2]*abs(u)+1)/((p[2]*abs(u)+1)^2+(p[3]^2)*h^2)^((3)/2)}####Gneiting (2002), combina fun1, fun2 y psi en Gneiting#####
#fun1
phi1=function(r,c,gama,v){v*exp(-c*r^gama)} #c>0, 0<gama<=1, siempre v=1
phi2=function(r,c,gama,v){((2^(v-1))*gamma(v))^(-1)*(c*r^0.5)^v*besselK(c*r^0.5,v)} #c>0, v>0
phi3=function(r,c,gama,v){(1+c*r^gama)^(-v)} #c>0, 0<gama<=1, v>0
phi4=function(r,c,gama,v){gama*(2^v)*(exp(c*r^0.5)+exp(-c*r^0.5))^(-v)} #c>0, v>0, siempre gama=1#fun2
psi1=function(r,a,alpha,beta){(a*r^alpha+1)^beta} #a>0, 0<alpha<=1, 0<=beta<=1
psi2=function(r,a,alpha,beta){log(a*r^alpha+beta)/log(beta)} #a>0, beta>1, 0<alpha<=1
psi3=function(r,a,alpha,beta){(a*r^alpha+beta)/(beta*(a*r^alpha+1))} #a>0, 0<beta<=1 0<alpha<=1 #Cualquier combinaci?n genera una funci?n de covarianza v?lida
Gneiting=function(h,u,sigma,d,a,alpha,beta,c,gama,v,psi,phi){(sigma^2/(psi((abs(u)^2),a,alpha,beta))^(d/2))*phi(h^2/(psi(abs(u)^2,a,alpha,beta)),c,gama,v)}#el caso mas general de Gneiting (2002) es cuando d=2, entonces queda
Gneiting=function(h,u,sigma,a,alpha,beta,c,gama,v,psi,phi){(sigma^2/(psi((abs(u)^2),a,alpha,beta)))*phi(h^2/(psi(abs(u)^2,a,alpha,beta)),c,gama,v)}####IACO_CESSARE
C_IACO_CESSARE=function(h,u,sigma,a,b,alpha,beta,gama){(1 + (h/a)^alpha + (u/b)^beta)^(-gama)}#(Porcu, 2007) Basado en la funci?n de supervivencia de Dagum
#funci?n de Dagum
Dagum=function(r,lambda,theta,epsilon){1-1/(1+lambda*r^(-theta))^epsilon} #lamdba, theta in (0,7), epsilon in (0,7)
Dagumm=function(r,lambda,theta,epsilon){ifelse(r==0,1,Dagum(r,lambda,theta,epsilon))}
Porcu_sep=function(h,u,lambda_h,theta_h,epsilon_h,lambda_u,theta_u,epsilon_u){Dagumm(h,lambda_h,theta_h,epsilon_h)*Dagumm(u,lambda_u,theta_u,epsilon_u)}
Porcu_Nsep=function(h,u,lambda_h,theta_h,epsilon_h,lambda_u,theta_u,epsilon_u,vartheta){vartheta*Dagumm(h,lambda_h,theta_h,epsilon_h)+(1-vartheta)*Dagumm(u,lambda_u,theta_u,epsilon_u)}1.2 CH 1 no separable
###CH 1 no separable
library(mvtnorm)#generar la grilla espacio temporal
x1 <- seq(0,30,by = 5)
x2 <- seq(10,60,by = 7)
t <- seq(1,20,len=10)
grillaSpT=expand.grid(x1,x2,t)
matDistSp=as.matrix(dist(grillaSpT[,1:2]))
matDistT=as.matrix(dist(grillaSpT[,3:3]))##parameters p, mu, que en este caso son p=c(7,2,1) y mu=120
sigma=cressie1(matDistSp,matDistT,p=c(7,2,1))
sim1=rmvnorm(1,mean=rep(120,nrow(grillaSpT)), sigma=sigma)
datos1=cbind(grillaSpT,t(sim1))names(datos1)=c("x","y","t","z((x,y),t)")
#View(datos1)
grillaSp=expand.grid(x1,x2)
colnames(grillaSp)=c("x","y")
rownames(grillaSp)=paste("S",1:nrow(grillaSp))
datos1_ord=datos1[order(datos1$x, datos1$y, datos1$t),]
dataSim1=matrix(c(datos1_ord[,4]),nrow=length(t),ncol=nrow(grillaSp),byrow=F)
colnames(dataSim1)=rownames(grillaSp)
rownames(dataSim1)=t
write.table(dataSim1,"dataSim1.txt")“” CH 2 no sepaarable
#CH 2 no separable
library(mvtnorm)#generar la grilla espacio temporal
x1 <- seq(0,30,by = 6)
x2 <- seq(10,60,by = 8)
t <- seq(1,20,len=10)
grillaSpT=expand.grid(x1,x2,t)
matDistSp=as.matrix(dist(grillaSpT[,1:2]))
matDistT=as.matrix(dist(grillaSpT[,3:3]))##parameters p, mu, que en este caso son p=c(7,2,1) y mu=120
sigma=CH_2(matDistSp,matDistT,p=c(10,3,4))
sim2=rmvnorm(1,mean=rep(34,nrow(grillaSpT)), sigma=sigma)
datos2=cbind(grillaSpT,t(sim2))
names(datos2)=c("x","y","t","zz((x,y),t)")
#View(datos2)
grillaSp=expand.grid(x1,x2)
colnames(grillaSp)=c("x","y")
rownames(grillaSp)=paste("S",1:nrow(grillaSp))
datos2_ord=datos2[order(datos2$x, datos2$y, datos2$t),]
dataSim2=matrix(c(datos2_ord[,4]),nrow=length(t),ncol=nrow(grillaSp),byrow=F)
colnames(dataSim2)=rownames(grillaSp)
rownames(dataSim2)=t
write.table(dataSim2,"dataSim2.txt")
class(dataSim2)## [1] "matrix" "array"1.3 CH3 no separable
#CH 3 no separable
x1 <- seq(0,30,by = 5)
x2 <- seq(10,60,by = 7)
grillaSp=expand.grid(x1,x2)
colnames(grillaSp)=c("x","y")
rownames(grillaSp)=paste("S",1:nrow(grillaSp))
t <- seq(1,20,len=10)
grillaSpT=expand.grid(x1,x2,t)
matDistSp=as.matrix(dist(grillaSpT[,1:2]))
matDistT=as.matrix(dist(grillaSpT[,3:3]))##parameters p, mu, que en este caso son p=c(7,2,1) y mu=120
sigma=CH_3(matDistSp,matDistT,p=c(6,2.5,3.2))
sim3=rmvnorm(1,mean=rep(34,nrow(grillaSpT)), sigma=sigma)
datos2=cbind(grillaSpT,t(sim3))
names(datos2)=c("x","y","t","zz((x,y),t)")#View(datos2)
datos3 = datos2
datos3_ord=datos3[order(datos3$x, datos3$y, datos3$t),]
dataSim3=matrix(c(datos3_ord[,4]),nrow=length(t),ncol=nrow(grillaSp),byrow=F)
colnames(dataSim3)=rownames(grillaSp)
rownames(dataSim3)=t1.4 CH 4
#caso 4
library(mvtnorm)#generar la grilla espacio temporal
x1 <- seq(1,35,by = 7)
x2 <- seq(10,60,by = 10)
grillaSp=expand.grid(x1,x2)
colnames(grillaSp)=c("x","y")
rownames(grillaSp)=paste("S",1:nrow(grillaSp))
t <- seq(1,20,len=10)
grillaSpT=expand.grid(x1,x2,t)
matDistSp=as.matrix(dist(grillaSpT[,1:2]))
matDistT=as.matrix(dist(grillaSpT[,3:3]))##parameters p, mu, que en este caso son p=c(7,2,1) y mu=120
sigma=CH_3(matDistSp,matDistT,p=c(6,2.5,3.2))
sim4=rmvnorm(1,mean=rep(34,nrow(grillaSpT)), sigma=sigma)
datos4=cbind(grillaSpT,t(sim4))
names(datos4)=c("x","y","t","zz((x,y),t)")#View(datos4)
datos4_ord=datos4[order(datos4$x, datos4$y, datos4$t),]
dataSim4=matrix(c(datos4_ord[,4]),nrow=length(t),ncol=nrow(grillaSp),byrow=F)
colnames(dataSim4)=rownames(grillaSp)
rownames(dataSim4)=t2 Spatial modeling leukemia
2.1 Mortality
Spatial modeling of incidence and mortality childhood leukemia based on Colombian armed conflict and poverty for children born during the years 2002-2013
2.1.1 Packages Mortality
rm(list=ls())
require(rgdal)
require(pscl)
require(sf)
require(spdep)
require(spatialreg) #test.W, scores.listw
require(stringr)
require(performance)
require(AER)
require(ggplot2)
require(vcdExtra)
require(dbscan)2.1.2 Code Mortality
- Reading the shapefile of 1124 Colombian municipalities, defining the Coordinate Reference System and centroid and building some variables
#Reading the shapefile of 1124 Colombian municipalities
muncol <- rgdal::readOGR(dsn="Armed_Conflict_Vs_Leukemia/muncol.shp")## OGR data source with driver: ESRI Shapefile
## Source: "/home/martha/Documentos/Cursos EE UN/Armed_Conflict_Vs_Leukemia/muncol.shp", layer: "muncol"
## with 1124 features
## It has 17 fieldsmuncol=spTransform(muncol,CRS("+init=epsg:21897"))
(l <- length(muncol))## [1] 1124#Representative coordinate (centroid)
options(warn = -1)
xy0=data.frame(x=muncol$x,y=muncol$y)
coordinates(xy0) <- c('x','y')
proj4string(xy0) <- CRS("+init=epsg:4326")
xy0=spTransform(xy0,CRS("+init=epsg:21897"))
###Loops for avoiding NA
r <- sum(muncol$Ndeaths)/sum(muncol$NPop)
for (i in 1:l){
if(muncol$NPop[i]==0){
muncol$EsperadosDeNCancer[i] <- 1
}
else{
muncol$EsperadosDeNCancer[i] <- muncol$NPop[i]*r
}
}
muncol$IICA_Cat=muncol$IICA_Ca
muncol$IICA_Cat=str_replace_all(muncol$IICA_Cat,"Bajo", "Low")
muncol$IICA_Cat=str_replace_all(muncol$IICA_Cat,"Medio", "Medium")
muncol$IICA_CatLow=ifelse(muncol$IICA_Cat=="Low",1,0)
muncol$IICA_CatMed=ifelse(muncol$IICA_Cat=="Medium",1,0)
muncol$IICA_High=as.character(1-(muncol$IICA_CatLow+muncol$IICA_CatMed))
muncol$UBN=muncol$NBI- Modeling leukemia Mortality Rate (LR) in terms of Colombian armed conflict index, poverty, rurality and health coverage. First, the usual Poisson regression model with mortality rate as response variable is estimated.
glmbaseLMR<-glm(Ndeaths ~IICA_High+UBN+Per_Rur+Cobertura+offset(log(EsperadosDeNCancer)), family = poisson,data = muncol)
anova(glmbaseLMR)## Analysis of Deviance Table
##
## Model: poisson, link: log
##
## Response: Ndeaths
##
## Terms added sequentially (first to last)
##
##
## Df Deviance Resid. Df Resid. Dev
## NULL 1123 799.92
## IICA_High 1 0.694 1122 799.22
## UBN 1 43.405 1121 755.82
## Per_Rur 1 4.017 1120 751.80
## Cobertura 1 9.185 1119 742.62muncol$residLMR=residuals(glmbaseLMR)
summary(glmbaseLMR)##
## Call:
## glm(formula = Ndeaths ~ IICA_High + UBN + Per_Rur + Cobertura +
## offset(log(EsperadosDeNCancer)), family = poisson, data = muncol)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.9317 -0.5949 -0.4108 -0.2389 3.3300
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -0.583783 0.307508 -1.898 0.05764 .
## IICA_High1 0.107822 0.084777 1.272 0.20343
## UBN -0.007902 0.003003 -2.632 0.00850 **
## Per_Rur -0.002705 0.002370 -1.141 0.25380
## Cobertura 0.991687 0.336039 2.951 0.00317 **
## ---
## Signif. codes:
## 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for poisson family taken to be 1)
##
## Null deviance: 799.92 on 1123 degrees of freedom
## Residual deviance: 742.62 on 1119 degrees of freedom
## AIC: 1271.7
##
## Number of Fisher Scoring iterations: 6Rurality and conflict armed index are not statistically significant in this first auxiliar model. However, we maintain these variables in the rest of the analysis and review its significance in the final model.
Checking excess zeros by comparison between the number of zeros predicted by the model with the observed number of zeros. Also checking overdispersion.
mu_LMR <- predict(glmbaseLMR, type = "response") # predict expected mean count
expLMR <- sum(dpois(x = 0, lambda = mu_LMR)) # sum the probabilities of a zero count for each mean
round(expLMR) #predicted number of zeros## [1] 898sum(muncol$Ndeaths < 1) #observed number of zeros## [1] 907zero.test(muncol$Ndeaths) #score test (van den Broek, 1995)## Score test for zero inflation
##
## Chi-square = 902.95398
## df = 1
## pvalue: < 0.000000000000000222##Checking overdispersion
dispersiontest(glmbaseLMR) #Cameron & Trivedi (1990)##
## Overdispersion test
##
## data: glmbaseLMR
## z = 2.2049, p-value = 0.01373
## alternative hypothesis: true dispersion is greater than 1
## sample estimates:
## dispersion
## 1.109361The observed frequency of zeroes in data exceeds the predicted in the Leukemia mortality rate (LMR) model. Also, overdispersion is detected.
Now, to validate the independence assumption, first, it is necessary to define spatial weighting possible matrices.
rook_nb_b=nb2listw(poly2nb(muncol,queen=FALSE), style="B",zero.policy = TRUE)
rook_nb_w=nb2listw(poly2nb(muncol,queen=FALSE), style="W",zero.policy = TRUE)
queen_nb_b=nb2listw(poly2nb(muncol,queen=TRUE), style="B",zero.policy = TRUE)
queen_nb_w=nb2listw(poly2nb(muncol,queen=TRUE), style="W",zero.policy = TRUE)
#Graphs neighbours
trinb=tri2nb(xy0)
options(warn = -1)
tri_nb_b=nb2listw(tri2nb(xy0), style="B",zero.policy = TRUE)
tri_nb_w=nb2listw(tri2nb(xy0), style="W",zero.policy = TRUE)
soi_nb_b=nb2listw(graph2nb(soi.graph(trinb,xy0)), style="B",zero.policy = TRUE)
soi_nb_w=nb2listw(graph2nb(soi.graph(trinb,xy0)), style="W",zero.policy = TRUE)
relative_nb_b=nb2listw(graph2nb(relativeneigh(xy0), sym=TRUE), style="B",zero.policy = TRUE)
relative_nb_w=nb2listw(graph2nb(relativeneigh(xy0), sym=TRUE), style="W",zero.policy = TRUE)
gabriel_nb_b=nb2listw(graph2nb(gabrielneigh(xy0), sym=TRUE), style="B",zero.policy = TRUE)
gabriel_nb_w=nb2listw(graph2nb(gabrielneigh(xy0), sym=TRUE), style="W",zero.policy = TRUE)
#Distance neighbours
knn1_nb_b=nb2listw(knn2nb(knearneigh(xy0, k = 1)), style="B",zero.policy = TRUE)
knn1_nb_w=nb2listw(knn2nb(knearneigh(xy0, k = 1)), style="W",zero.policy = TRUE)
knn2_nb_b=nb2listw(knn2nb(knearneigh(xy0, k = 2)), style="B",zero.policy = TRUE)
knn2_nb_w=nb2listw(knn2nb(knearneigh(xy0, k = 2)), style="W",zero.policy = TRUE)
knn3_nb_b=nb2listw(knn2nb(knearneigh(xy0, k = 3)), style="B",zero.policy = TRUE)
knn3_nb_w=nb2listw(knn2nb(knearneigh(xy0, k = 3)), style="W",zero.policy = TRUE)
knn4_nb_b=nb2listw(knn2nb(knearneigh(xy0, k = 4)), style="B",zero.policy = TRUE)
knn4_nb_w=nb2listw(knn2nb(knearneigh(xy0, k = 4)), style="W",zero.policy = TRUE)
mat=list(rook_nb_b,rook_nb_w,
queen_nb_b,queen_nb_w,
tri_nb_b,tri_nb_w,
soi_nb_b,soi_nb_w,
gabriel_nb_b,gabriel_nb_w,
relative_nb_b,relative_nb_w,
knn1_nb_b,knn1_nb_w,
knn2_nb_b,knn2_nb_w,
knn3_nb_b,knn3_nb_w,
knn4_nb_b,knn4_nb_w)- Testing spatial autocorrelation using Moran index test based on weighting matrices built in the last step. Note that with all weighting matrices we obtain a significant spatial autocorrelation.
aux=numeric(0)
options(warn = -1)
{
for(i in 1:length(mat))
aux[i]=moran.test(muncol$residLMR,mat[[i]],alternative="two.sided")$"statistic"
aux
} ## [1] 1.238996 1.473832 1.428553 1.629968 1.367192 1.592464
## [7] 1.921616 2.011106 1.860100 2.247294 2.629440 2.588622
## [13] 1.099401 1.099401 2.469062 2.469062 3.088200 3.088200
## [19] 3.450986 3.450986which.max(aux)## [1] 19moran.test(muncol$residLMR, mat[[which.max(aux)]], alternative="two.sided")##
## Moran I test under randomisation
##
## data: muncol$residLMR
## weights: mat[[which.max(aux)]]
##
## Moran I statistic standard deviate = 3.451, p-value =
## 0.0005585
## alternative hypothesis: two.sided
## sample estimates:
## Moran I statistic Expectation Variance
## 0.0672352967 -0.0008904720 0.0003897053- First, Poisson Hurdle model is estimated without consider spatial autocorrelation.
mod.hurdleLMR <- hurdle(Ndeaths ~IICA_High+UBN+Per_Rur+Cobertura+offset(log(EsperadosDeNCancer))|IICA_High+UBN+Per_Rur+Cobertura+offset(log(EsperadosDeNCancer)),data = muncol,dist = "poisson", zero.dist = "binomial")
resid_Pois_Hurdle=residuals(mod.hurdleLMR,"response")
summary(mod.hurdleLMR)##
## Call:
## hurdle(formula = Ndeaths ~ IICA_High + UBN + Per_Rur +
## Cobertura + offset(log(EsperadosDeNCancer)) | IICA_High +
## UBN + Per_Rur + Cobertura + offset(log(EsperadosDeNCancer)),
## data = muncol, dist = "poisson", zero.dist = "binomial")
##
## Pearson residuals:
## Min 1Q Median 3Q Max
## -1.6105 -0.4155 -0.2926 -0.1781 7.8519
##
## Count model coefficients (truncated poisson with log link):
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 0.0131708 0.3793725 0.035 0.9723
## IICA_High1 0.2239159 0.1048208 2.136 0.0327 *
## UBN -0.0006294 0.0050823 -0.124 0.9014
## Per_Rur -0.0064173 0.0049162 -1.305 0.1918
## Cobertura 0.1702217 0.4227398 0.403 0.6872
## Zero hurdle model coefficients (binomial with logit link):
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.013658 0.570592 -1.777 0.075650 .
## IICA_High1 -0.091317 0.177363 -0.515 0.606652
## UBN -0.011792 0.004690 -2.514 0.011928 *
## Per_Rur -0.005190 0.003982 -1.303 0.192473
## Cobertura 2.283308 0.624231 3.658 0.000254 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Number of iterations in BFGS optimization: 10
## Log-likelihood: -624 on 10 DfpR2(mod.hurdleLMR)## fitting null model for pseudo-r2## llh llhNull G2 McFadden
## -623.9804020 -1369.2239672 1490.4871304 0.5442817
## r2ML r2CU
## 0.7344776 0.8048896moran.test(resid_Pois_Hurdle, mat[[which.max(aux)]], alternative="two.sided")##
## Moran I test under randomisation
##
## data: resid_Pois_Hurdle
## weights: mat[[which.max(aux)]]
##
## Moran I statistic standard deviate = 4.8924, p-value
## = 0.0000009964
## alternative hypothesis: two.sided
## sample estimates:
## Moran I statistic Expectation Variance
## 0.0935041340 -0.0008904720 0.0003722701- Only Conflict armed index predictor is significant but model residuals are significantly spatially autocorrelated. So, we use spatial filtering and check significance again. Below we find Moran Eigenvectors.
MEpoisLMR <- spatialreg::ME(Ndeaths ~ IICA_High+UBN+Per_Rur+Cobertura+offset(log(EsperadosDeNCancer)),data=muncol,family="poisson",listw=knn4_nb_b, alpha=0.02, verbose=TRUE)## eV[,11], I: 0.02918226 ZI: NA, pr(ZI): 0.08MoranEigenVLMR=data.frame(fitted(MEpoisLMR))
#summary(MoranEigenVLMR)- Now, we used Poisson Hurdle model to manage the overdispersion due to zero excess and Moran eigenfunctions are included as additional explanatory variables, so that spatial autocorrelation is considered.
mod.hurdleLMR <- hurdle(Ndeaths ~IICA_High+UBN+Per_Rur+Cobertura+fitted(MEpoisLMR)+offset(log(EsperadosDeNCancer))|IICA_High+UBN+Per_Rur+Cobertura+offset(log(EsperadosDeNCancer)),data = muncol,dist = "poisson", zero.dist = "binomial")
resid_Pois_Hurdle=residuals(mod.hurdleLMR,"response")
summary(mod.hurdleLMR)##
## Call:
## hurdle(formula = Ndeaths ~ IICA_High + UBN + Per_Rur +
## Cobertura + fitted(MEpoisLMR) + offset(log(EsperadosDeNCancer)) |
## IICA_High + UBN + Per_Rur + Cobertura + offset(log(EsperadosDeNCancer)),
## data = muncol, dist = "poisson", zero.dist = "binomial")
##
## Pearson residuals:
## Min 1Q Median 3Q Max
## -1.6969 -0.4153 -0.2920 -0.1791 7.8744
##
## Count model coefficients (truncated poisson with log link):
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 0.374295 0.391853 0.955 0.33948
## IICA_High1 0.286868 0.104433 2.747 0.00602
## UBN -0.010727 0.005917 -1.813 0.06986
## Per_Rur -0.003464 0.005096 -0.680 0.49664
## Cobertura -0.058726 0.436141 -0.135 0.89289
## fitted(MEpoisLMR) -8.856022 1.670191 -5.302 0.000000114
##
## (Intercept)
## IICA_High1 **
## UBN .
## Per_Rur
## Cobertura
## fitted(MEpoisLMR) ***
## Zero hurdle model coefficients (binomial with logit link):
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.013658 0.570592 -1.777 0.075650 .
## IICA_High1 -0.091317 0.177363 -0.515 0.606652
## UBN -0.011792 0.004690 -2.514 0.011928 *
## Per_Rur -0.005190 0.003982 -1.303 0.192473
## Cobertura 2.283308 0.624231 3.658 0.000254 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Number of iterations in BFGS optimization: 12
## Log-likelihood: -610 on 11 DfpR2(mod.hurdleLMR)## fitting null model for pseudo-r2## llh llhNull G2 McFadden
## -610.0288758 -1369.2239672 1518.3901828 0.5544711
## r2ML r2CU
## 0.7409880 0.8120241moran.test(resid_Pois_Hurdle, mat[[which.max(aux)]], alternative="two.sided")##
## Moran I test under randomisation
##
## data: resid_Pois_Hurdle
## weights: mat[[which.max(aux)]]
##
## Moran I statistic standard deviate = 1.4546, p-value
## = 0.1458
## alternative hypothesis: two.sided
## sample estimates:
## Moran I statistic Expectation Variance
## 0.027522708 -0.000890472 0.000381564- Rurality and health coverage are not statistically significant for counto model. So, those predictors are excluded of the spatial filtering and model.
MEpoisLMR <- spatialreg::ME(Ndeaths ~ IICA_High+UBN+offset(log(EsperadosDeNCancer)),data=muncol,family="poisson",listw=knn4_nb_b, alpha=0.02, verbose=TRUE)## eV[,11], I: 0.01071212 ZI: NA, pr(ZI): 0.3MoranEigenVLMR=data.frame(fitted(MEpoisLMR))
#summary(MoranEigenVLMR)mod.hurdleLMR <- hurdle(Ndeaths ~IICA_High+UBN+fitted(MEpoisLMR)+offset(log(EsperadosDeNCancer))|UBN+Cobertura+offset(log(EsperadosDeNCancer)),data = muncol,dist = "poisson", zero.dist = "binomial")
summary(mod.hurdleLMR)##
## Call:
## hurdle(formula = Ndeaths ~ IICA_High + UBN + fitted(MEpoisLMR) +
## offset(log(EsperadosDeNCancer)) | UBN + Cobertura +
## offset(log(EsperadosDeNCancer)), data = muncol,
## dist = "poisson", zero.dist = "binomial")
##
## Pearson residuals:
## Min 1Q Median 3Q Max
## -1.5905 -0.4184 -0.2973 -0.1823 7.3265
##
## Count model coefficients (truncated poisson with log link):
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 0.355460 0.097724 3.637 0.000275
## IICA_High1 0.274468 0.100011 2.744 0.006062
## UBN -0.013803 0.003796 -3.636 0.000277
## fitted(MEpoisLMR) -9.134355 1.617421 -5.647 0.0000000163
##
## (Intercept) ***
## IICA_High1 **
## UBN ***
## fitted(MEpoisLMR) ***
## Zero hurdle model coefficients (binomial with logit link):
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.279352 0.535993 -2.387 0.016992 *
## UBN -0.014391 0.004288 -3.356 0.000789 ***
## Cobertura 2.354642 0.616661 3.818 0.000134 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Number of iterations in BFGS optimization: 11
## Log-likelihood: -611.3 on 7 DfpR2(mod.hurdleLMR)## fitting null model for pseudo-r2## llh llhNull G2 McFadden
## -611.2637930 -1369.2239672 1515.9203483 0.5535692
## r2ML r2CU
## 0.7404182 0.8113997moran.test(resid_Pois_Hurdle, mat[[which.max(aux)]], alternative="two.sided")##
## Moran I test under randomisation
##
## data: resid_Pois_Hurdle
## weights: mat[[which.max(aux)]]
##
## Moran I statistic standard deviate = 1.4546, p-value
## = 0.1458
## alternative hypothesis: two.sided
## sample estimates:
## Moran I statistic Expectation Variance
## 0.027522708 -0.000890472 0.000381564- Now, Poisson-Hurdle model residuals are not significant spatially autocorrelated. The LMR’s positive values depend only on the Index of armed conflict (IICA) and on the unsatisfied basic needs index (UBN) and LMR’s zero values depend on the UBN and health coverage. Note that the model shows good performance, according to pseudo R2 and the comparison between observed and predicted frequencies.
mf <- model.frame(mod.hurdleLMR)
y <- model.response(mf)
w <- model.weights(mf)
if(is.null(w)) w <- rep(1, NROW(y))
max0 <- 20L
obs <- as.vector(xtabs(w ~ factor(y, levels = 0L:max0)))
exp <- colSums(predict(mod.hurdleLMR, type = "prob", at = 0L:max0) * w)
fitted_vs_observed <- data.frame(Expected = exp,
Observed = obs)
data <- reshape2::melt(fitted_vs_observed)## No id variables; using all as measure variablesdata <- data.frame(data, x = 0:20)
data1 <- data[1:21, ]
data2 <- data[22:42, ]
pMortality <- ggplot() +
geom_line(data1, mapping = aes(x = x, y = value, group = variable
, color = variable)) +
geom_point(data1, mapping = aes(x = x, y = value, group = variable,
color = variable)) +
geom_col(data2, mapping = aes(x = x, y = value, group = variable),
alpha = 0.7) +
theme_light() +
labs(x = "Number of deaths",
y = "Frecuencies")
pMortality
2.2 Incidence
Spatial modeling of incidence and mortality childhood leukemia based on Colombian armed conflict and poverty for children born during the years 2002-2013
2.2.1 Packages Incidence
rm(list=ls())
require(rgdal)
require(pscl)
require(sf)
require(spdep)
require(spatialreg) #test.W, scores.listw
require(stringr)
require(performance)
require(AER)
require(ggplot2)
require(vcdExtra)2.2.2 Code Incidence
- Reading the shapefile of 1124 Colombian municipalities, defining the Coordinate Reference System and centroid and building some variables
#Reading the shapefile of 1124 Colombian municipalities
muncol <- rgdal::readOGR(dsn="Armed_Conflict_Vs_Leukemia/muncol.shp")## OGR data source with driver: ESRI Shapefile
## Source: "/home/martha/Documentos/Cursos EE UN/Armed_Conflict_Vs_Leukemia/muncol.shp", layer: "muncol"
## with 1124 features
## It has 17 fieldsmuncol=spTransform(muncol,CRS("+init=epsg:21897"))
(l <- length(muncol))## [1] 1124#Representative coordinate (centroid)
xy0=data.frame(x=muncol$x,y=muncol$y)
coordinates(xy0) <- c('x','y')
proj4string(xy0) <- CRS("+init=epsg:4326")
xy0=spTransform(xy0,CRS("+init=epsg:21897"))
###Loops for avoiding NA
r <- sum(muncol$NCases)/sum(muncol$NPop)
for (i in 1:l){
if(muncol$NPop[i]==0){
muncol$EsperadosNCancer[i] <- 1
}
else{
muncol$EsperadosNCancer[i] <- muncol$NPop[i]*r
}
}
muncol$IICA_Cat=muncol$IICA_Ca
muncol$IICA_Cat=str_replace_all(muncol$IICA_Cat,"Bajo", "Low")
muncol$IICA_Cat=str_replace_all(muncol$IICA_Cat,"Medio", "Medium")
muncol$IICA_CatLow=ifelse(muncol$IICA_Cat=="Low",1,0)
muncol$IICA_CatMed=ifelse(muncol$IICA_Cat=="Medium",1,0)
muncol$IICA_High=as.character(1-(muncol$IICA_CatLow+muncol$IICA_CatMed))
muncol$UBN=muncol$NBI- Modeling leukemia Incidence Rate (LR) in terms of Colombian armed conflict index, poverty and rurality. First, the usual Poisson regression model with incidence rate as response variable is estimated.
glmbaseLR<-glm(NCases ~IICA_High+UBN+Per_Rur+offset(log(EsperadosNCancer)), family = poisson,data = muncol)
anova(glmbaseLR)## Analysis of Deviance Table
##
## Model: poisson, link: log
##
## Response: NCases
##
## Terms added sequentially (first to last)
##
##
## Df Deviance Resid. Df Resid. Dev
## NULL 1123 2524.9
## IICA_High 1 0.75 1122 2524.1
## UBN 1 328.90 1121 2195.2
## Per_Rur 1 0.11 1120 2195.1summary(glmbaseLR)##
## Call:
## glm(formula = NCases ~ IICA_High + UBN + Per_Rur + offset(log(EsperadosNCancer)),
## family = poisson, data = muncol)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -5.1779 -1.1632 -0.5270 0.6082 7.7193
##
## Coefficients:
## Estimate Std. Error z value
## (Intercept) 0.3226036 0.0276280 11.677
## IICA_High1 0.0818208 0.0294297 2.780
## UBN -0.0123797 0.0010425 -11.875
## Per_Rur -0.0002510 0.0007692 -0.326
## Pr(>|z|)
## (Intercept) < 0.0000000000000002 ***
## IICA_High1 0.00543 **
## UBN < 0.0000000000000002 ***
## Per_Rur 0.74419
## ---
## Signif. codes:
## 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for poisson family taken to be 1)
##
## Null deviance: 2524.9 on 1123 degrees of freedom
## Residual deviance: 2195.1 on 1120 degrees of freedom
## AIC: 4174.2
##
## Number of Fisher Scoring iterations: 5muncol$residLR=residuals(glmbaseLR)Rurality is not statistically significant in this first auxiliar model. However, we maintain this variable in the rest of the analysis and review its significance in the final model.
Checking excess zeros by comparison between the number of zeros predicted by the model with the observed number of zeros. Also checking overdispersion.
mu_LR <- predict(glmbaseLR, type = "response") # predict expected mean count
expLR <- sum(dpois(x = 0, lambda = mu_LR)) # sum the probabilities of a zero count for each mean
round(expLR) #predicted number of zeros## [1] 382sum(muncol$NCases < 1) #observed number of zeros## [1] 443zero.test(muncol$NCases) #score test (van den Broek, 1995)## Score test for zero inflation
##
## Chi-square = 12268.7129
## df = 1
## pvalue: < 0.000000000000000222##Checking overdispersion
dispersiontest(glmbaseLR) #Cameron & Trivedi (1990)##
## Overdispersion test
##
## data: glmbaseLR
## z = 4.1887, p-value = 0.00001403
## alternative hypothesis: true dispersion is greater than 1
## sample estimates:
## dispersion
## 2.309041check_overdispersion(glmbaseLR) #Gelman and Hill (2007)## # Overdispersion test
##
## dispersion ratio = 2.431
## Pearson's Chi-Squared = 2722.353
## p-value = < 0.001## Overdispersion detected.The observed frequency of zeroes in data exceeds the predicted in the Leukemia incidence rate (LR) model. Also, overdispersion is detected.
Now, to validate the independence assumption, first, it is necessary to define spatial weighting possible matrices.
rook_nb_b=nb2listw(poly2nb(muncol,queen=FALSE), style="B",zero.policy = TRUE)
rook_nb_w=nb2listw(poly2nb(muncol,queen=FALSE), style="W",zero.policy = TRUE)
queen_nb_b=nb2listw(poly2nb(muncol,queen=TRUE), style="B",zero.policy = TRUE)
queen_nb_w=nb2listw(poly2nb(muncol,queen=TRUE), style="W",zero.policy = TRUE)
#Graphs neighbours
trinb=tri2nb(xy0)
options(warn = -1)
tri_nb_b=nb2listw(tri2nb(xy0), style="B",zero.policy = TRUE)
tri_nb_w=nb2listw(tri2nb(xy0), style="W",zero.policy = TRUE)
soi_nb_b=nb2listw(graph2nb(soi.graph(trinb,xy0)), style="B",zero.policy = TRUE)
soi_nb_w=nb2listw(graph2nb(soi.graph(trinb,xy0)), style="W",zero.policy = TRUE)
relative_nb_b=nb2listw(graph2nb(relativeneigh(xy0), sym=TRUE), style="B",zero.policy = TRUE)
relative_nb_w=nb2listw(graph2nb(relativeneigh(xy0), sym=TRUE), style="W",zero.policy = TRUE)
gabriel_nb_b=nb2listw(graph2nb(gabrielneigh(xy0), sym=TRUE), style="B",zero.policy = TRUE)
gabriel_nb_w=nb2listw(graph2nb(gabrielneigh(xy0), sym=TRUE), style="W",zero.policy = TRUE)
#Distance neighbours
knn1_nb_b=nb2listw(knn2nb(knearneigh(xy0, k = 1)), style="B",zero.policy = TRUE)
knn1_nb_w=nb2listw(knn2nb(knearneigh(xy0, k = 1)), style="W",zero.policy = TRUE)
knn2_nb_b=nb2listw(knn2nb(knearneigh(xy0, k = 2)), style="B",zero.policy = TRUE)
knn2_nb_w=nb2listw(knn2nb(knearneigh(xy0, k = 2)), style="W",zero.policy = TRUE)
knn3_nb_b=nb2listw(knn2nb(knearneigh(xy0, k = 3)), style="B",zero.policy = TRUE)
knn3_nb_w=nb2listw(knn2nb(knearneigh(xy0, k = 3)), style="W",zero.policy = TRUE)
knn4_nb_b=nb2listw(knn2nb(knearneigh(xy0, k = 4)), style="B",zero.policy = TRUE)
knn4_nb_w=nb2listw(knn2nb(knearneigh(xy0, k = 4)), style="W",zero.policy = TRUE)
knn6_nb_b=nb2listw(knn2nb(knearneigh(xy0, k = 6)), style="B",zero.policy = TRUE)
knn6_nb_w=nb2listw(knn2nb(knearneigh(xy0, k = 6)), style="W",zero.policy = TRUE)
mat=list(rook_nb_b,rook_nb_w,
queen_nb_b,queen_nb_w,
tri_nb_b,tri_nb_w,
soi_nb_b,soi_nb_w,
gabriel_nb_b,gabriel_nb_w,
relative_nb_b,relative_nb_w,
knn1_nb_b,knn1_nb_w,
knn2_nb_b,knn2_nb_w,
knn3_nb_b,knn3_nb_w,
knn4_nb_b,knn4_nb_w,
knn6_nb_b,knn6_nb_w)- Testing spatial autocorrelation using Moran index test based on weighting matrices built in the last step. Note that with all weighting matrices we obtain a significant spatial autocorrelation.
aux=numeric(0)
options(warn = -1)
{
for(i in 1:length(mat))
aux[i]=moran.test(muncol$residLR,mat[[i]],alternative="two.sided")$"p"
}
aux## [1] 0.0000000017764454223 0.0000000000163053411
## [3] 0.0000000011162954779 0.0000000000340919650
## [5] 0.0000000002619438209 0.0000000000198490005
## [7] 0.0000000000280007352 0.0000000000264847296
## [9] 0.0000000000707310275 0.0000000000040680047
## [11] 0.0000000013453360945 0.0000000058676552459
## [13] 0.0006342820038119282 0.0006342820038119282
## [15] 0.0000000053378560647 0.0000000053378560647
## [17] 0.0000000000046536598 0.0000000000046536598
## [19] 0.0000000000002138542 0.0000000000002138542
## [21] 0.0000000000005932765 0.0000000000005932765moran.test(muncol$residLR, mat[[which.max(aux)]], alternative="two.sided")##
## Moran I test under randomisation
##
## data: muncol$residLR
## weights: mat[[which.max(aux)]]
##
## Moran I statistic standard deviate = 3.4165, p-value
## = 0.0006343
## alternative hypothesis: two.sided
## sample estimates:
## Moran I statistic Expectation Variance
## 0.123653792 -0.000890472 0.001328865- First, Poisson Hurdle model is estimated without consider spatial autocorrelation.
mod.hurdleLR <- hurdle(NCases ~IICA_High+UBN+Per_Rur+offset(log(EsperadosNCancer))|IICA_High+UBN+Per_Rur+offset(log(EsperadosNCancer)),data = muncol,dist = "poisson", zero.dist = "binomial")
resid_Pois_Hurdle=residuals(mod.hurdleLR,"response")
summary(mod.hurdleLR)##
## Call:
## hurdle(formula = NCases ~ IICA_High + UBN + Per_Rur +
## offset(log(EsperadosNCancer)) | IICA_High + UBN +
## Per_Rur + offset(log(EsperadosNCancer)), data = muncol,
## dist = "poisson", zero.dist = "binomial")
##
## Pearson residuals:
## Min 1Q Median 3Q Max
## -3.6935 -0.7943 -0.3775 0.6266 17.7799
##
## Count model coefficients (truncated poisson with log link):
## Estimate Std. Error z value
## (Intercept) 0.3151943 0.0289252 10.897
## IICA_High1 0.0769858 0.0309613 2.487
## UBN -0.0123171 0.0011548 -10.666
## Per_Rur 0.0020604 0.0008876 2.321
## Pr(>|z|)
## (Intercept) <0.0000000000000002 ***
## IICA_High1 0.0129 *
## UBN <0.0000000000000002 ***
## Per_Rur 0.0203 *
## Zero hurdle model coefficients (binomial with logit link):
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 1.001514 0.249402 4.016 0.0000593 ***
## IICA_High1 0.072259 0.137921 0.524 0.600
## UBN -0.013830 0.003541 -3.906 0.0000939 ***
## Per_Rur -0.004660 0.003364 -1.385 0.166
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Number of iterations in BFGS optimization: 9
## Log-likelihood: -2051 on 8 DfpR2(mod.hurdleLR)## fitting null model for pseudo-r2## llh llhNull G2 McFadden
## -2051.4697559 -9229.3509481 14355.7623845 0.7777233
## r2ML r2CU
## 0.9999972 0.9999972moran.test(resid_Pois_Hurdle, mat[[which.max(aux)]], alternative="two.sided")##
## Moran I test under randomisation
##
## data: resid_Pois_Hurdle
## weights: mat[[which.max(aux)]]
##
## Moran I statistic standard deviate = 4.5053, p-value
## = 0.000006627
## alternative hypothesis: two.sided
## sample estimates:
## Moran I statistic Expectation Variance
## 0.158812671 -0.000890472 0.001256531- Thus, residuals are significantly spatially autocorrelated. So, we are going tu use spatial filtering. Below we find Moran Eigenvectors.
MEpoisLR <- spatialreg::ME(NCases ~ IICA_High+UBN+Per_Rur+offset(log(EsperadosNCancer)),data=muncol,family="poisson",listw=mat[[3]], alpha=0.02, verbose=TRUE)## eV[,29], I: 0.01179903 ZI: NA, pr(ZI): 0.23MoranEigenVLR=data.frame(fitted(MEpoisLR))- Now, we used Poisson Hurdle model to manage the overdispersion due to zero excess and Moran eigenfunctions are included as additional explanatory variables, so that spatial autocorrelation is considered.
mod.hurdleLR <- hurdle(NCases ~IICA_High+UBN+Per_Rur+fitted(MEpoisLR)+offset(log(EsperadosNCancer))|Per_Rur+offset(log(EsperadosNCancer)),data = muncol,dist = "poisson", zero.dist = "binomial")
resid_Pois_Hurdle=residuals(mod.hurdleLR,"response")
moran.test(resid_Pois_Hurdle, mat[[3]], alternative="two.sided")##
## Moran I test under randomisation
##
## data: resid_Pois_Hurdle
## weights: mat[[3]]
##
## Moran I statistic standard deviate = 1.0424, p-value
## = 0.2972
## alternative hypothesis: two.sided
## sample estimates:
## Moran I statistic Expectation Variance
## 0.0162024286 -0.0008904720 0.0002689009summary(mod.hurdleLR)##
## Call:
## hurdle(formula = NCases ~ IICA_High + UBN + Per_Rur +
## fitted(MEpoisLR) + offset(log(EsperadosNCancer)) |
## Per_Rur + offset(log(EsperadosNCancer)), data = muncol,
## dist = "poisson", zero.dist = "binomial")
##
## Pearson residuals:
## Min 1Q Median 3Q Max
## -3.2263 -0.7927 -0.3875 0.6339 17.8272
##
## Count model coefficients (truncated poisson with log link):
## Estimate Std. Error z value
## (Intercept) 0.2275843 0.0328678 6.924
## IICA_High1 0.1568024 0.0342051 4.584
## UBN -0.0113328 0.0011644 -9.733
## Per_Rur 0.0016899 0.0008965 1.885
## fitted(MEpoisLR) 2.6540637 0.4767638 5.567
## Pr(>|z|)
## (Intercept) 0.00000000000438 ***
## IICA_High1 0.00000455776769 ***
## UBN < 0.0000000000000002 ***
## Per_Rur 0.0594 .
## fitted(MEpoisLR) 0.00000002594128 ***
## Zero hurdle model coefficients (binomial with logit link):
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 0.646903 0.213106 3.036 0.0024 **
## Per_Rur -0.008731 0.003237 -2.697 0.0070 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Number of iterations in BFGS optimization: 10
## Log-likelihood: -2044 on 7 DfpR2(mod.hurdleLR)## fitting null model for pseudo-r2## llh llhNull G2 McFadden
## -2043.6785123 -9229.3509481 14371.3448717 0.7785675
## r2ML r2CU
## 0.9999972 0.9999973- Rurality is not statistically significant to explain the Leukemia incidence rate. The only predictor statistically significant for zeroes model is rurality. In addition, the Spatial filtering results are the same without this variable.
MEpoisLR <- spatialreg::ME(NCases ~ IICA_High+UBN+offset(log(EsperadosNCancer)),data=muncol,family="poisson",listw=mat[[3]], alpha=0.02, verbose=TRUE)## eV[,29], I: 0.01112525 ZI: NA, pr(ZI): 0.14MoranEigenVLR=data.frame(fitted(MEpoisLR))
mod.hurdleLR <- hurdle(NCases ~IICA_High+UBN+fitted(MEpoisLR)+offset(log(EsperadosNCancer))|Per_Rur+offset(log(EsperadosNCancer)),data = muncol,dist = "poisson", zero.dist = "binomial")
resid_Pois_Hurdle=residuals(mod.hurdleLR,"response")
moran.test(resid_Pois_Hurdle, mat[[3]], alternative="two.sided")##
## Moran I test under randomisation
##
## data: resid_Pois_Hurdle
## weights: mat[[3]]
##
## Moran I statistic standard deviate = 1.2484, p-value
## = 0.2119
## alternative hypothesis: two.sided
## sample estimates:
## Moran I statistic Expectation Variance
## 0.0194478991 -0.0008904720 0.0002654261summary(mod.hurdleLR)##
## Call:
## hurdle(formula = NCases ~ IICA_High + UBN + fitted(MEpoisLR) +
## offset(log(EsperadosNCancer)) | Per_Rur + offset(log(EsperadosNCancer)),
## data = muncol, dist = "poisson", zero.dist = "binomial")
##
## Pearson residuals:
## Min 1Q Median 3Q Max
## -3.3173 -0.7976 -0.3786 0.6607 18.2757
##
## Count model coefficients (truncated poisson with log link):
## Estimate Std. Error z value
## (Intercept) 0.2143974 0.0321264 6.674
## IICA_High1 0.1700350 0.0335266 5.072
## UBN -0.0097928 0.0008191 -11.955
## fitted(MEpoisLR) 2.7262303 0.4759204 5.728
## Pr(>|z|)
## (Intercept) 0.000000000025 ***
## IICA_High1 0.000000394376 ***
## UBN < 0.0000000000000002 ***
## fitted(MEpoisLR) 0.000000010142 ***
## Zero hurdle model coefficients (binomial with logit link):
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 0.646903 0.213106 3.036 0.0024 **
## Per_Rur -0.008731 0.003237 -2.697 0.0070 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Number of iterations in BFGS optimization: 9
## Log-likelihood: -2045 on 6 DfpR2(mod.hurdleLR)## fitting null model for pseudo-r2## llh llhNull G2 McFadden
## -2045.4283395 -9229.3509481 14367.8452173 0.7783779
## r2ML r2CU
## 0.9999972 0.9999973- Hence, Poisson-Hurdle model residuals are not significant spatially autocorrelated. The LR’s positive values depend only on the Index of armed conflict (IICA) and on the unsatisfied basic needs index (UBN) and its zero values depend on the rurality. Note that the model shows good performance, according to pseudo R2 and the comparison between observed and predicted frequencies.
mf <- model.frame(mod.hurdleLR)
y <- model.response(mf)
w <- model.weights(mf)
if(is.null(w)) w <- rep(1, NROW(y))
max0 <- 20L
obs <- as.vector(xtabs(w ~ factor(y, levels = 0L:max0)))
exp <- colSums(predict(mod.hurdleLR, type = "prob", at = 0L:max0) * w)
fitted_vs_observed <- data.frame(Expected = exp,
Observed = obs)
data <- reshape2::melt(fitted_vs_observed)## No id variables; using all as measure variablesdata <- data.frame(data, x = 0:20)
data1 <- data[1:21, ]
data2 <- data[22:42, ]
pl1 <- ggplot() +
geom_line(data1, mapping = aes(x = x, y = value, group = variable
, color = variable)) +
geom_point(data1, mapping = aes(x = x, y = value, group = variable,
color = variable)) +
geom_col(data2, mapping = aes(x = x, y = value, group = variable),
alpha = 0.7) +
theme_light() +
labs(x = "Number of cases",
y = "Frecuencies")
pl1
3 Modelos de regresión espacial
3.1 Estudio de Mercadeo
Se comparan varios tipos de modelos de regresión espacial para ver con cual se obtiene el mejor ajuste. Se consideran modelos autoregresivos y de medias móvviles así como su combinación.
3.2 Paquetes
rm(list=ls())
library(openxlsx)
library(dplyr)
library(rgdal)
library(maptools)
library(GISTools)
library(spdep)
library(readr)
library(car)
library(readxl)
library(psych)
library(rgdal)
library(FactoClass)
library(spdep)
require("GWmodel")
library("mapsRinteractive")
options(scipen = 999)3.3 Lectura de Datos
# Lectura de Datos
BASE <- read_excel("Trabajo Grado/BASE.xlsx")
# Lectura del Shape de Colombia por Departamentos
Colombia = readOGR(dsn = "Trabajo Grado/Geodatabase Colombia", layer = "departamentos")## OGR data source with driver: ESRI Shapefile
## Source: "/home/martha/Documentos/Cursos EE UN/Trabajo Grado/Geodatabase Colombia", layer: "departamentos"
## with 33 features
## It has 6 fields
## Integer64 fields read as strings: AñO_CREAC4 Pre-procesamiento de datos
#Cruce de información con el shape cargado
Insumo = merge(Colombia, BASE, by.x="COD_DANE", by.y="Cod")
Insumo = subset(Insumo[c(1:31,33),])
# Conversión a Coordenadas UTM
Crs.geo = CRS("+proj=tmerc +lat_0=4.599047222222222 +lon_0=-74.08091666666667 +k=1 +x_0=1000000 +y_0=1000000 +ellps=intl +towgs84=307,304,-318,0,0,0,0 +units=m +no_defs")
proj4string(Insumo) <- Crs.geo
Insumo.utm = spTransform(Insumo, CRS("+init=epsg:3724 +units=km"))4.1 Matriz de vecindades
#---
# MATRIZ DE VECINDADES (W)
#---
## Centroides de las Áreas
Centros = getSpPPolygonsLabptSlots(Insumo.utm)
Centroids <- SpatialPointsDataFrame(coords = Centros, data=Insumo.utm@data,
proj4string=CRS("+init=epsg:3724 +units=km"))
# Matriz de Distancias entre los Centriodes
Wdist = dist(Centros, up=T)
# Matriz W de vecindades
library(pgirmess)
library(HistogramTools)
library(strucchange)
library(spdep)
Insumo.nb = poly2nb(Insumo.utm, queen=T)
#n <- max(sapply(Insumo.nb, length))
#ll <- lapply(Insumo.nb, function(X) {
# c(as.numeric(X), rep(0, times = n - length(X)))
#})
#out <- do.call(cbind, ll)
#Departamentos<-Insumo$Departamento
#MatW<-matrix(NA,32,32)
#for (i in 1:8) {
# for (j in 1:32) {
# if (out[i,j]!=0) {
# MatW[out[i,j],j]<-1
# } else{MatW[out[i,j],j]<-0}
# }
#}
#for (i in 1:32) {
# for (j in 1:32) {
# if (is.na(MatW[i,j])) {
# MatW[i,j]<-0
# }
# }
#}
#colnames(MatW)<-Departamentos
#rownames(MatW)<-Departamentos
#MatW1<-MatW[,1:16]
#MatW2<-MatW[,17:32]
# Martiz W (Estilos)
Insumo.lw = nb2listw(Insumo.nb)
Insumo.lwb = nb2listw(Insumo.nb, style="B")
Insumo.lwc = nb2listw(Insumo.nb, style="C")
Insumo.lwu = nb2listw(Insumo.nb, style="U")
Insumo.lww = nb2listw(Insumo.nb, style="W")4.2 Mapa de valores observados
# Mapa de Valores Observados
#dev.new() #windows()
choropleth(Insumo, Insumo$CAP_BAC)
shad = auto.shading(Insumo$CAP_BAC, n=5, cols=(brewer.pal(5,"Reds")), cutter = quantileCuts)
choro.legend(1555874,535165.5, shad, fmt="%1.1f", title = "Valores Locales", cex=0.7, under = "Menos de", between = "a", over = "Mas de")
title("Valores Observados para las captaciones del banco agrario
en Colombia, cuarto trimestre 2020", cex.main=1)
map.scale(755874,335165.5, 250000, "km", 2, 50, sfcol='brown')
4.3 Pruebas de Autocorrelación
#----------------------------
# PRUEBAS DE AUTOCORRELACION
#----------------------------
# Moran
moran.test(Insumo$CAP_BAC, Insumo.lw)##
## Moran I test under randomisation
##
## data: Insumo$CAP_BAC
## weights: Insumo.lw
##
## Moran I statistic standard deviate = 2.0024, p-value
## = 0.02262
## alternative hypothesis: greater
## sample estimates:
## Moran I statistic Expectation Variance
## 0.153081266 -0.032258065 0.008566935# Dispersograma de Moran
#dev.new() #windows()
moran.plot(Insumo$CAP_BAC, Insumo.lw, labels=as.character(Insumo$Departamento), xlab="Captaciones BAC", ylab="Captaciones BAC rezagado", las=1, pch=16, cex=0.5)
legend("bottomright", legend=c("I de Moran: 0.1530", "Valor P: 0.02262"), cex=1,bg='lightgreen')
title("Dispersograma de Moran para las captaciones del banco agrario en
los Departamentos de Colombia, cuarto trimestre 2020", cex.main=1)
# Local G
nearng = dnearneigh(coordinates(Insumo.utm), 0, 550)
Insumo.lw.g = nb2listw(nearng, style="B")
localG = localG(Insumo$CAP_BAC, Insumo.lw.g); localG## [1] 1.66525050 0.02608278 1.33032949 1.15892050
## [5] 1.85852161 0.68445519 1.49486468 0.10163662
## [9] 1.64717068 1.32714028 2.53361281 2.21899396
## [13] -0.71311540 0.50952811 1.48899277 0.81676480
## [17] 0.98434717 2.09087184 2.08725553 1.05493906
## [21] 1.32486118 2.09147517 2.16305539 1.89323276
## [25] 1.52155929 0.84992902 -1.19798594 -1.33847805
## [29] 0.29701426 -1.60300117 1.67015910 1.96543367
## attr(,"cluster")
## [1] High Low Low High Low Low High Low Low High Low
## [12] High Low Low Low High High Low Low High Low High
## [23] High Low Low Low Low Low Low Low Low High
## Levels: Low High
## attr(,"gstari")
## [1] FALSE
## attr(,"call")
## localG(x = Insumo$CAP_BAC, listw = Insumo.lw.g)
## attr(,"class")
## [1] "localG"# Simulaci?n montecarlo
sim.G = matrix(0,1000,32)
for(i in 1:1000) sim.G[i,] = localG(sample(Insumo$CAP_BAC),Insumo.lw.g)
mc.pvalor.G = (colSums(sweep(sim.G,2,localG,">="))+1)/(nrow(sim.G)+1)
mc.pvalor.G## [1] 0.009990010 0.438561439 0.086913087 0.114885115
## [5] 0.001998002 0.288711289 0.067932068 0.442557443
## [9] 0.031968032 0.055944056 0.000999001 0.001998002
## [13] 0.709290709 0.303696304 0.034965035 0.235764236
## [17] 0.168831169 0.000999001 0.000999001 0.127872128
## [21] 0.090909091 0.000999001 0.004995005 0.016983017
## [25] 0.051948052 0.228771229 0.969030969 0.963036963
## [29] 0.430569431 0.994005994 0.053946054 0.0009990014.4 Mapas
# Mapas
par(mfrow=c(1,2), mar=c(1,1,8,1)/2)
shadeg = auto.shading(localG, n=5, cols=(brewer.pal(5,"Purples")), cutter=quantileCuts)
#dev.new() #windows()
choropleth(Insumo, localG, shading=shadeg)
choro.legend(1555874,535165.5, shadeg, fmt="%1.2f", title = "G", cex=0.7, under = "Menos de", between = "a", over = "Mas de")
title("G Getis Ord Local para las captaciones del banco agrario
en Colombia, cuarto trimestre 2020", cex.main=1)
map.scale(755874,335165.5, 250000, "km", 2, 50, sfcol='brown')
# Mapa de P-values
#dev.new() #windows()
shadegp = shading(c(0.01,0.05,0.1), cols = (brewer.pal(4,"Spectral")))
choropleth(Insumo, mc.pvalor.G, shading=shadegp)
choro.legend(1555874,535165.5, shadegp, fmt="%1.2f", title = "P-valor de G", cex=0.7, under = "Menos de", between = "a", over = "Mas de")
title("P- Valor de G Getis Ord Local para las captaciones del banco agrario
en Colombia, cuarto trimestre 2020", cex.main=1)
map.scale(755874,335165.5, 250000, "km", 2, 50, sfcol='brown')
##Modelos SDEM, SDM, Manski, SARAR
####Modelos SDEM, SDM, Manski, SARAR########
#reg.eq1=CAP_BAC ~ PIB + NBI + CAP_BOG + CAP_BC + CAP_OCC + CAP_CS + Población + IPM
reg.eq1=CAP_BAC ~ PIB + NBI + CAP_BOG+CAP_BC + CAP_OCC + CAP_CS+ Población
reg1=lm(reg.eq1,data=Insumo) #OLS y=XB+e,
reg2=lmSLX(reg.eq1,data=Insumo, Insumo.lw) #SLX y=XB+WxT+e
reg3=lagsarlm(reg.eq1,data= Insumo, Insumo.lw) #Lag Y y=XB+WxT+u, u=LWu+e
reg4=errorsarlm(reg.eq1,data=Insumo, Insumo.lw) #Spatial Error y=pWy+XB+e
reg5=errorsarlm(reg.eq1, data=Insumo, Insumo.lw, etype="emixed") #SDEM Spatial Durbin Error Model y=XB+WxT+u, u=LWu+e
reg6=lagsarlm(reg.eq1, data=Insumo,Insumo.lw, type="mixed") #SDM Spatial Durbin Model (add lag X to SAR) y=pWy+XB+WXT+e
reg7=sacsarlm(reg.eq1,data=Insumo, Insumo.lw, type="sacmixed") #Manski Model: y=pWy+XB+WXT+u, u=LWu+e (no recomendado)
reg8=sacsarlm(reg.eq1,data=Insumo,Insumo.lw, type="sac") #SARAR o Kelejian-Prucha, Cliff-Ord, o SAC If all T=0,y=pWy+XB+u, u=LWu+e4.5 Resumen de modelos
#Resumen de modelos
s=summary
s(reg1)#OLS##
## Call:
## lm(formula = reg.eq1, data = Insumo)
##
## Residuals:
## Min 1Q Median 3Q Max
## -276.51 -65.60 -7.76 46.60 396.20
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 148.21380364 79.80068638 1.857 0.0756 .
## PIB 0.00389642 0.00328986 1.184 0.2479
## NBI -1.28539812 1.73982368 -0.739 0.4672
## CAP_BOG -0.06643826 0.05411306 -1.228 0.2314
## CAP_BC 0.00397406 0.00607852 0.654 0.5195
## CAP_OCC -0.04340185 0.02170799 -1.999 0.0570 .
## CAP_CS 0.47283237 0.31370238 1.507 0.1448
## Población 0.00000137 0.00006700 0.020 0.9839
## ---
## Signif. codes:
## 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 141.6 on 24 degrees of freedom
## Multiple R-squared: 0.8807, Adjusted R-squared: 0.8459
## F-statistic: 25.31 on 7 and 24 DF, p-value: 0.000000001309s(reg2)#SLX##
## Call:
## lm(formula = formula(paste("y ~ ", paste(colnames(x)[-1], collapse = "+"))),
## data = as.data.frame(x), weights = weights)
##
## Residuals:
## Min 1Q Median 3Q Max
## -201.00 -74.99 -0.51 34.55 342.00
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 392.97159157 284.42668099 1.382 0.185
## PIB 0.00429319 0.00383973 1.118 0.279
## NBI -0.57603773 2.48213535 -0.232 0.819
## CAP_BOG -0.00703635 0.07700761 -0.091 0.928
## CAP_BC -0.00075536 0.01003615 -0.075 0.941
## CAP_OCC -0.05372016 0.03418522 -1.571 0.135
## CAP_CS 0.12199794 0.43670734 0.279 0.783
## Población 0.00004753 0.00012149 0.391 0.701
## lag.PIB 0.00317318 0.00943185 0.336 0.741
## lag.NBI -6.81433196 5.99552430 -1.137 0.271
## lag.CAP_BOG -0.06868663 0.18842513 -0.365 0.720
## lag.CAP_BC 0.00684589 0.01472675 0.465 0.648
## lag.CAP_OCC -0.00984285 0.05447122 -0.181 0.859
## lag.CAP_CS 0.33585267 1.09533771 0.307 0.763
## lag.Población -0.00016927 0.00017459 -0.970 0.346
##
## Residual standard error: 151.6 on 17 degrees of freedom
## Multiple R-squared: 0.9031, Adjusted R-squared: 0.8234
## F-statistic: 11.32 on 14 and 17 DF, p-value: 0.000005467s(reg3)#Lag Y##
## Call:
## lagsarlm(formula = reg.eq1, data = Insumo, listw = Insumo.lw)
##
## Residuals:
## Min 1Q Median 3Q Max
## -213.859 -60.238 -17.811 42.960 393.389
##
## Type: lag
## Coefficients: (numerical Hessian approximate standard errors)
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 77.75431737089 74.33304193262 1.0460 0.29555
## PIB 0.00330780479 0.00157831647 2.0958 0.03610
## NBI -0.77863469452 1.48478285166 -0.5244 0.59999
## CAP_BOG -0.05466121822 0.04352388108 -1.2559 0.20916
## CAP_BC 0.00533211204 0.00466472729 1.1431 0.25301
## CAP_OCC -0.03421667740 0.01731007390 -1.9767 0.04808
## CAP_CS 0.40699816555 0.26036918467 1.5632 0.11802
## Población 0.00000091508 NaN NaN NaN
##
## Rho: 0.22884, LR test value: 2.096, p-value: 0.14768
## Approximate (numerical Hessian) standard error: 0.15346
## z-value: 1.4912, p-value: 0.1359
## Wald statistic: 2.2237, p-value: 0.1359
##
## Log likelihood: -198.251 for lag model
## ML residual variance (sigma squared): 13916, (sigma: 117.97)
## Number of observations: 32
## Number of parameters estimated: 10
## AIC: 416.5, (AIC for lm: 416.6)s(reg4)#Lag Error (SEM)##
## Call:
## errorsarlm(formula = reg.eq1, data = Insumo, listw = Insumo.lw)
##
## Residuals:
## Min 1Q Median 3Q Max
## -215.7428 -56.4299 -2.2091 46.6630 425.7867
##
## Type: error
## Coefficients: (asymptotic standard errors)
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 94.500067067 73.097738551 1.2928 0.19608
## PIB 0.003656790 0.002619923 1.3958 0.16279
## NBI -0.334674368 1.408551018 -0.2376 0.81219
## CAP_BOG -0.032484044 0.049990128 -0.6498 0.51582
## CAP_BC 0.001202333 0.005555428 0.2164 0.82866
## CAP_OCC -0.048739698 0.019538015 -2.4946 0.01261
## CAP_CS 0.285572491 0.287233643 0.9942 0.32012
## Población 0.000040164 0.000066648 0.6026 0.54676
##
## Lambda: 0.50692, LR test value: 3.8031, p-value: 0.051158
## Approximate (numerical Hessian) standard error: 0.21479
## z-value: 2.3601, p-value: 0.018271
## Wald statistic: 5.57, p-value: 0.018271
##
## Log likelihood: -197.3975 for error model
## ML residual variance (sigma squared): 12495, (sigma: 111.78)
## Number of observations: 32
## Number of parameters estimated: 10
## AIC: 414.79, (AIC for lm: 416.6)s(reg5)#Durbin Error (SDEM)##
## Call:
## errorsarlm(formula = reg.eq1, data = Insumo, listw = Insumo.lw,
## etype = "emixed")
##
## Residuals:
## Min 1Q Median 3Q Max
## -199.7723 -69.8844 -2.0075 37.9235 362.9104
##
## Type: error
## Coefficients: (asymptotic standard errors)
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 248.934497490 220.997185179 1.1264 0.25999
## PIB 0.004499050 0.002763860 1.6278 0.10356
## NBI -0.058410888 1.767448320 -0.0330 0.97364
## CAP_BOG -0.026724643 0.054644416 -0.4891 0.62480
## CAP_BC -0.000183348 0.007104434 -0.0258 0.97941
## CAP_OCC -0.051006011 0.024157938 -2.1114 0.03474
## CAP_CS 0.227498808 0.309055946 0.7361 0.46166
## Población 0.000035177 0.000084525 0.4162 0.67729
## lag.PIB 0.003069904 0.007273446 0.4221 0.67297
## lag.NBI -4.397301264 4.370216212 -1.0062 0.31432
## lag.CAP_BOG -0.078935306 0.133353632 -0.5919 0.55390
## lag.CAP_BC 0.000970530 0.011031859 0.0880 0.92990
## lag.CAP_OCC -0.013417109 0.040319110 -0.3328 0.73931
## lag.CAP_CS 0.374124929 0.777502427 0.4812 0.63038
## lag.Población -0.000103911 0.000125213 -0.8299 0.40661
##
## Lambda: 0.28217, LR test value: 0.34013, p-value: 0.55976
## Approximate (numerical Hessian) standard error: 0.43008
## z-value: 0.6561, p-value: 0.51176
## Wald statistic: 0.43047, p-value: 0.51176
##
## Log likelihood: -195.7931 for error model
## ML residual variance (sigma squared): 11856, (sigma: 108.89)
## Number of observations: 32
## Number of parameters estimated: 17
## AIC: 425.59, (AIC for lm: 423.93)s(reg6)#Durbin (SDM)##
## Call:
## lagsarlm(formula = reg.eq1, data = Insumo, listw = Insumo.lw,
## type = "mixed")
##
## Residuals:
## Min 1Q Median 3Q Max
## -185.6170 -74.5630 -1.2308 34.6848 363.6597
##
## Type: mixed
## Coefficients: (numerical Hessian approximate standard errors)
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 259.002911178 230.104789400 1.1256 0.2603
## PIB 0.004292096 0.002709485 1.5841 0.1132
## NBI -0.068020334 1.599249655 -0.0425 0.9661
## CAP_BOG -0.013498834 0.053646345 -0.2516 0.8013
## CAP_BC -0.000674466 0.006747917 -0.1000 0.9204
## CAP_OCC -0.052995708 0.023276623 -2.2768 0.0228
## CAP_CS 0.159111963 0.305216541 0.5213 0.6022
## Población 0.000046528 0.000083888 0.5546 0.5791
## lag.PIB 0.001006280 0.006950379 0.1448 0.8849
## lag.NBI -5.022146095 4.504322175 -1.1150 0.2649
## lag.CAP_BOG -0.060141057 0.129919351 -0.4629 0.6434
## lag.CAP_BC 0.003372687 0.010806814 0.3121 0.7550
## lag.CAP_OCC 0.001941495 0.030122408 0.0645 0.9486
## lag.CAP_CS 0.265435969 0.754778096 0.3517 0.7251
## lag.Población -0.000120261 0.000126709 -0.9491 0.3426
##
## Rho: 0.28321, LR test value: 0.99104, p-value: 0.31949
## Approximate (numerical Hessian) standard error: 0.26808
## z-value: 1.0564, p-value: 0.29077
## Wald statistic: 1.116, p-value: 0.29077
##
## Log likelihood: -195.4676 for mixed model
## ML residual variance (sigma squared): 11616, (sigma: 107.78)
## Number of observations: 32
## Number of parameters estimated: 17
## AIC: 424.94, (AIC for lm: 423.93)s(reg7)#Manski##
## Call:
## sacsarlm(formula = reg.eq1, data = Insumo, listw = Insumo.lw,
## type = "sacmixed")
##
## Residuals:
## Min 1Q Median 3Q Max
## -179.6048 -72.7882 -2.7818 33.8501 346.2488
##
## Type: sacmixed
## Coefficients: (numerical Hessian approximate standard errors)
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 307.899524851 284.687742330 1.0815 0.27946
## PIB 0.004070842 0.002887831 1.4097 0.15864
## NBI -0.195254185 2.070147473 -0.0943 0.92486
## CAP_BOG 0.002531850 0.093292487 0.0271 0.97835
## CAP_BC -0.001838769 0.009686163 -0.1898 0.84944
## CAP_OCC -0.056119738 0.028995161 -1.9355 0.05293
## CAP_CS 0.071595235 0.518838438 0.1380 0.89025
## Población 0.000065749 0.000127955 0.5138 0.60736
## lag.PIB 0.000817609 0.006904128 0.1184 0.90573
## lag.NBI -6.096432794 5.600016244 -1.0886 0.27631
## lag.CAP_BOG -0.052377434 0.137793679 -0.3801 0.70386
## lag.CAP_BC 0.006801659 0.017044912 0.3990 0.68986
## lag.CAP_OCC 0.008763485 0.047596659 0.1841 0.85392
## lag.CAP_CS 0.219189297 0.801371640 0.2735 0.78446
## lag.Población -0.000162608 0.000228334 -0.7122 0.47637
##
## Rho: 0.38485
## Approximate (numerical Hessian) standard error: 0.37355
## z-value: 1.0303, p-value: 0.30289
## Lambda: -0.26343
## Approximate (numerical Hessian) standard error: 0.83838
## z-value: -0.31421, p-value: 0.75336
##
## LR test value: 7.7816, p-value: 0.5563
##
## Log likelihood: -195.4082 for sacmixed model
## ML residual variance (sigma squared): 11213, (sigma: 105.89)
## Number of observations: 32
## Number of parameters estimated: 18
## AIC: 426.82, (AIC for lm: 416.6)s(reg8)#SARAR lag Y and lag e (SAC)##
## Call:
## sacsarlm(formula = reg.eq1, data = Insumo, listw = Insumo.lw,
## type = "sac")
##
## Residuals:
## Min 1Q Median 3Q Max
## -203.1991 -58.2427 -4.1109 46.5336 421.1733
##
## Type: sac
## Coefficients: (numerical Hessian approximate standard errors)
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 73.149386015 83.375351447 0.8774 0.38030
## PIB 0.003487952 0.002657617 1.3124 0.18937
## NBI -0.337466937 1.455345658 -0.2319 0.81663
## CAP_BOG -0.038888663 0.051472319 -0.7555 0.44993
## CAP_BC 0.002799262 0.006135570 0.4562 0.64822
## CAP_OCC -0.043084476 0.021726659 -1.9830 0.04736
## CAP_CS 0.320438586 0.295160199 1.0856 0.27764
## Población 0.000028476 0.000068297 0.4170 0.67671
##
## Rho: 0.1104
## Approximate (numerical Hessian) standard error: 0.19096
## z-value: 0.57817, p-value: 0.56315
## Lambda: 0.41973
## Approximate (numerical Hessian) standard error: 0.27372
## z-value: 1.5334, p-value: 0.12517
##
## LR test value: 4.1193, p-value: 0.1275
##
## Log likelihood: -197.2394 for sac model
## ML residual variance (sigma squared): 12624, (sigma: 112.36)
## Number of observations: 32
## Number of parameters estimated: 11
## AIC: 416.48, (AIC for lm: 416.6)4.6 Calculo de varibles significativas
#Calculo de variables signid¿ficativas
reg.eq2=CAP_BAC ~ PIB + CAP_BOG+CAP_BC + CAP_OCC + CAP_CS+ Población
reg4=errorsarlm(reg.eq2,data=Insumo, Insumo.lw)
s(reg4)#Lag Error (SEM)##
## Call:
## errorsarlm(formula = reg.eq2, data = Insumo, listw = Insumo.lw)
##
## Residuals:
## Min 1Q Median 3Q Max
## -211.1287 -54.9469 -1.1316 40.5690 428.8317
##
## Type: error
## Coefficients: (asymptotic standard errors)
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 82.780380448 57.200033358 1.4472 0.14784
## PIB 0.003786089 0.002550194 1.4846 0.13764
## CAP_BOG -0.033655761 0.049317358 -0.6824 0.49497
## CAP_BC 0.001072561 0.005563108 0.1928 0.84712
## CAP_OCC -0.049110630 0.019547548 -2.5124 0.01199
## CAP_CS 0.290079762 0.285013021 1.0178 0.30878
## Población 0.000039933 0.000066827 0.5976 0.55013
##
## Lambda: 0.51895, LR test value: 4.4697, p-value: 0.0345
## Approximate (numerical Hessian) standard error: 0.20433
## z-value: 2.5398, p-value: 0.011092
## Wald statistic: 6.4505, p-value: 0.011092
##
## Log likelihood: -197.4239 for error model
## ML residual variance (sigma squared): 12470, (sigma: 111.67)
## Number of observations: 32
## Number of parameters estimated: 9
## AIC: 412.85, (AIC for lm: 415.32)reg.eq3=CAP_BAC ~ PIB + CAP_BOG + CAP_OCC + CAP_CS+ Población
reg4=errorsarlm(reg.eq3,data=Insumo, Insumo.lw)
s(reg4)#Lag Error (SEM)##
## Call:
## errorsarlm(formula = reg.eq3, data = Insumo, listw = Insumo.lw)
##
## Residuals:
## Min 1Q Median 3Q Max
## -214.6537 -56.5893 -1.9568 41.1618 430.2455
##
## Type: error
## Coefficients: (asymptotic standard errors)
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 76.659389371 48.733986281 1.5730 0.1157149
## PIB 0.003936351 0.002412095 1.6319 0.1026960
## CAP_BOG -0.026724272 0.035542537 -0.7519 0.4521139
## CAP_OCC -0.051550780 0.014822573 -3.4779 0.0005054
## CAP_CS 0.249952777 0.204318664 1.2233 0.2211984
## Población 0.000047471 0.000055107 0.8614 0.3890008
##
## Lambda: 0.52489, LR test value: 4.7822, p-value: 0.028756
## Approximate (numerical Hessian) standard error: 0.19905
## z-value: 2.6369, p-value: 0.0083666
## Wald statistic: 6.9533, p-value: 0.0083666
##
## Log likelihood: -197.4421 for error model
## ML residual variance (sigma squared): 12461, (sigma: 111.63)
## Number of observations: 32
## Number of parameters estimated: 8
## AIC: 410.88, (AIC for lm: 413.67)reg.eq4=CAP_BAC ~ PIB + CAP_OCC + CAP_CS+ Población
reg4=errorsarlm(reg.eq4,data=Insumo, Insumo.lw)
s(reg4)#Lag Error (SEM)##
## Call:
## errorsarlm(formula = reg.eq4, data = Insumo, listw = Insumo.lw)
##
## Residuals:
## Min 1Q Median 3Q Max
## -200.4867 -63.5891 -8.8979 41.1675 444.7078
##
## Type: error
## Coefficients: (asymptotic standard errors)
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 78.047294926 51.760316072 1.5079 0.1315904
## PIB 0.003727043 0.002409110 1.5471 0.1218483
## CAP_OCC -0.050131489 0.014726792 -3.4041 0.0006638
## CAP_CS 0.099564078 0.037675929 2.6426 0.0082261
## Población 0.000057480 0.000053995 1.0646 0.2870778
##
## Lambda: 0.56286, LR test value: 6.894, p-value: 0.0086485
## Approximate (numerical Hessian) standard error: 0.17902
## z-value: 3.1441, p-value: 0.0016662
## Wald statistic: 9.8851, p-value: 0.0016662
##
## Log likelihood: -197.7004 for error model
## ML residual variance (sigma squared): 12505, (sigma: 111.82)
## Number of observations: 32
## Number of parameters estimated: 7
## AIC: 409.4, (AIC for lm: 414.29)reg.eq5=CAP_BAC ~ PIB + CAP_OCC + CAP_CS
reg4=errorsarlm(reg.eq5,data=Insumo, Insumo.lw)
s(reg4)#Lag Error (SEM)##
## Call:
## errorsarlm(formula = reg.eq5, data = Insumo, listw = Insumo.lw)
##
## Residuals:
## Min 1Q Median 3Q Max
## -189.815 -68.002 -13.434 35.002 443.595
##
## Type: error
## Coefficients: (asymptotic standard errors)
## Estimate Std. Error z value
## (Intercept) 100.98166025 46.44259466 2.1743
## PIB 0.00611113 0.00092889 6.5789
## CAP_OCC -0.04669321 0.01466331 -3.1844
## CAP_CS 0.07261035 0.02868558 2.5312
## Pr(>|z|)
## (Intercept) 0.029680
## PIB 0.00000000004738
## CAP_OCC 0.001451
## CAP_CS 0.011366
##
## Lambda: 0.54225, LR test value: 6.0083, p-value: 0.014239
## Asymptotic standard error: 0.17423
## z-value: 3.1123, p-value: 0.0018565
## Wald statistic: 9.6862, p-value: 0.0018565
##
## Log likelihood: -198.2513 for error model
## ML residual variance (sigma squared): 13034, (sigma: 114.17)
## Number of observations: 32
## Number of parameters estimated: 6
## AIC: 408.5, (AIC for lm: 412.51)4.7 Mapa Estimado
###Mapa estimado
fit = reg4$fitted.values
#dev.new() #windows()
shade.fit = shading(c(100,130,200,400), cols=(brewer.pal(5,"Reds")))
choropleth(Insumo, fit, shading=shade.fit)
choro.legend(1555874,535165.5, shade.fit, fmt="%1.2f", title = "Estimaciones", cex=0.7, under = "Menos de", between = "a", over = "Mas de")
title("Valores ajustados mediante el modelo SEM para las captaciones del banco agrario
en Colombia, cuarto trimestre 2020", cex.main=1)
map.scale(755874,335165.5, 250000, "km", 2, 50, sfcol='brown')
###R^2 Nagelkerke
# summary.sarlm(reg4,Nagelkerke = TRUE) TO-DO
###Test de moran residuales modelo SEM
moran.test(reg4$residuals, Insumo.lw)##
## Moran I test under randomisation
##
## data: reg4$residuals
## weights: Insumo.lw
##
## Moran I statistic standard deviate = 0.83723, p-value
## = 0.2012
## alternative hypothesis: greater
## sample estimates:
## Moran I statistic Expectation Variance
## 0.05266908 -0.03225806 0.01028984#Municipal
ColombiaM = readOGR(dsn = "Trabajo Grado/Geodatabase Colombia", layer = "municipios")## OGR data source with driver: ESRI Shapefile
## Source: "/home/martha/Documentos/Cursos EE UN/Trabajo Grado/Geodatabase Colombia", layer: "municipios"
## with 1107 features
## It has 6 fields
## Integer64 fields read as strings: COD_MUN COD_DEPTO5 Ilustración del kriging simple espacio tiempo
Martha Bohorquez
16/5/2022
5.2 Simulación no condicional de una realización de un campo aleatorio espacio temporal no separable usando el modelo de covarianza cressie1
En primer lugar, se generar la grilla espacio temporal. Aquí suponemos n=6 ubicaciones espaciales y T=4 momentos en el tiempo, así en total son 24 ubicaciones espacio-tiempo. Se llevará a cabo la simulación y posteriormente se usará el predictor kriging con su respectiva estimación de varianza del error de predicción, en un punto no “observado”. Se asume conocida la función de covarianza. En la práctica esta matriz se puede estimar por métodos como maxima veorsimilitud, pseudoverosimilitud y métodos basados en mínimos cuadrados.
x1 <- seq(0,3,len = 3)
x2 <- seq(1,6,len = 2)
t <- 1:4
grillaSpT=expand.grid(x1,x2,t)
#matriz de distancias (rezagos) espaciales
matDistSp=as.matrix(dist(grillaSpT[,1:2]))
#matriz de distancias (rezagos) temporales
matDistT=as.matrix(dist(grillaSpT[,3:3]))
cressie1=function(h,u,p){(p[1]^2/((p[2]^2*u^2+1)))*exp(-(p[3]^2*h^2)/(p[2]^2*u^2+1))}
##parámetros p, mu, que en este caso son p=c(0.4,1.7,1.9) y mu=0
sigma=cressie1(matDistSp,matDistT,p=c(0.15,1.7,1.9))
sim1=rmvnorm(1,mean=rep(0,nrow(grillaSpT)), sigma=sigma)
datos1=cbind(grillaSpT,t(sim1))
names(datos1)=c("x","y","t","z((x,y),t)")
matDistSp## 1 2 3 4 5 6
## 1 0.000000 1.500000 3.000000 5.000000 5.220153 5.830952
## 2 1.500000 0.000000 1.500000 5.220153 5.000000 5.220153
## 3 3.000000 1.500000 0.000000 5.830952 5.220153 5.000000
## 4 5.000000 5.220153 5.830952 0.000000 1.500000 3.000000
## 5 5.220153 5.000000 5.220153 1.500000 0.000000 1.500000
## 6 5.830952 5.220153 5.000000 3.000000 1.500000 0.000000
## 7 0.000000 1.500000 3.000000 5.000000 5.220153 5.830952
## 8 1.500000 0.000000 1.500000 5.220153 5.000000 5.220153
## 9 3.000000 1.500000 0.000000 5.830952 5.220153 5.000000
## 10 5.000000 5.220153 5.830952 0.000000 1.500000 3.000000
## 11 5.220153 5.000000 5.220153 1.500000 0.000000 1.500000
## 12 5.830952 5.220153 5.000000 3.000000 1.500000 0.000000
## 13 0.000000 1.500000 3.000000 5.000000 5.220153 5.830952
## 14 1.500000 0.000000 1.500000 5.220153 5.000000 5.220153
## 15 3.000000 1.500000 0.000000 5.830952 5.220153 5.000000
## 16 5.000000 5.220153 5.830952 0.000000 1.500000 3.000000
## 17 5.220153 5.000000 5.220153 1.500000 0.000000 1.500000
## 18 5.830952 5.220153 5.000000 3.000000 1.500000 0.000000
## 19 0.000000 1.500000 3.000000 5.000000 5.220153 5.830952
## 20 1.500000 0.000000 1.500000 5.220153 5.000000 5.220153
## 21 3.000000 1.500000 0.000000 5.830952 5.220153 5.000000
## 22 5.000000 5.220153 5.830952 0.000000 1.500000 3.000000
## 23 5.220153 5.000000 5.220153 1.500000 0.000000 1.500000
## 24 5.830952 5.220153 5.000000 3.000000 1.500000 0.000000
## 7 8 9 10 11 12
## 1 0.000000 1.500000 3.000000 5.000000 5.220153 5.830952
## 2 1.500000 0.000000 1.500000 5.220153 5.000000 5.220153
## 3 3.000000 1.500000 0.000000 5.830952 5.220153 5.000000
## 4 5.000000 5.220153 5.830952 0.000000 1.500000 3.000000
## 5 5.220153 5.000000 5.220153 1.500000 0.000000 1.500000
## 6 5.830952 5.220153 5.000000 3.000000 1.500000 0.000000
## 7 0.000000 1.500000 3.000000 5.000000 5.220153 5.830952
## 8 1.500000 0.000000 1.500000 5.220153 5.000000 5.220153
## 9 3.000000 1.500000 0.000000 5.830952 5.220153 5.000000
## 10 5.000000 5.220153 5.830952 0.000000 1.500000 3.000000
## 11 5.220153 5.000000 5.220153 1.500000 0.000000 1.500000
## 12 5.830952 5.220153 5.000000 3.000000 1.500000 0.000000
## 13 0.000000 1.500000 3.000000 5.000000 5.220153 5.830952
## 14 1.500000 0.000000 1.500000 5.220153 5.000000 5.220153
## 15 3.000000 1.500000 0.000000 5.830952 5.220153 5.000000
## 16 5.000000 5.220153 5.830952 0.000000 1.500000 3.000000
## 17 5.220153 5.000000 5.220153 1.500000 0.000000 1.500000
## 18 5.830952 5.220153 5.000000 3.000000 1.500000 0.000000
## 19 0.000000 1.500000 3.000000 5.000000 5.220153 5.830952
## 20 1.500000 0.000000 1.500000 5.220153 5.000000 5.220153
## 21 3.000000 1.500000 0.000000 5.830952 5.220153 5.000000
## 22 5.000000 5.220153 5.830952 0.000000 1.500000 3.000000
## 23 5.220153 5.000000 5.220153 1.500000 0.000000 1.500000
## 24 5.830952 5.220153 5.000000 3.000000 1.500000 0.000000
## 13 14 15 16 17 18
## 1 0.000000 1.500000 3.000000 5.000000 5.220153 5.830952
## 2 1.500000 0.000000 1.500000 5.220153 5.000000 5.220153
## 3 3.000000 1.500000 0.000000 5.830952 5.220153 5.000000
## 4 5.000000 5.220153 5.830952 0.000000 1.500000 3.000000
## 5 5.220153 5.000000 5.220153 1.500000 0.000000 1.500000
## 6 5.830952 5.220153 5.000000 3.000000 1.500000 0.000000
## 7 0.000000 1.500000 3.000000 5.000000 5.220153 5.830952
## 8 1.500000 0.000000 1.500000 5.220153 5.000000 5.220153
## 9 3.000000 1.500000 0.000000 5.830952 5.220153 5.000000
## 10 5.000000 5.220153 5.830952 0.000000 1.500000 3.000000
## 11 5.220153 5.000000 5.220153 1.500000 0.000000 1.500000
## 12 5.830952 5.220153 5.000000 3.000000 1.500000 0.000000
## 13 0.000000 1.500000 3.000000 5.000000 5.220153 5.830952
## 14 1.500000 0.000000 1.500000 5.220153 5.000000 5.220153
## 15 3.000000 1.500000 0.000000 5.830952 5.220153 5.000000
## 16 5.000000 5.220153 5.830952 0.000000 1.500000 3.000000
## 17 5.220153 5.000000 5.220153 1.500000 0.000000 1.500000
## 18 5.830952 5.220153 5.000000 3.000000 1.500000 0.000000
## 19 0.000000 1.500000 3.000000 5.000000 5.220153 5.830952
## 20 1.500000 0.000000 1.500000 5.220153 5.000000 5.220153
## 21 3.000000 1.500000 0.000000 5.830952 5.220153 5.000000
## 22 5.000000 5.220153 5.830952 0.000000 1.500000 3.000000
## 23 5.220153 5.000000 5.220153 1.500000 0.000000 1.500000
## 24 5.830952 5.220153 5.000000 3.000000 1.500000 0.000000
## 19 20 21 22 23 24
## 1 0.000000 1.500000 3.000000 5.000000 5.220153 5.830952
## 2 1.500000 0.000000 1.500000 5.220153 5.000000 5.220153
## 3 3.000000 1.500000 0.000000 5.830952 5.220153 5.000000
## 4 5.000000 5.220153 5.830952 0.000000 1.500000 3.000000
## 5 5.220153 5.000000 5.220153 1.500000 0.000000 1.500000
## 6 5.830952 5.220153 5.000000 3.000000 1.500000 0.000000
## 7 0.000000 1.500000 3.000000 5.000000 5.220153 5.830952
## 8 1.500000 0.000000 1.500000 5.220153 5.000000 5.220153
## 9 3.000000 1.500000 0.000000 5.830952 5.220153 5.000000
## 10 5.000000 5.220153 5.830952 0.000000 1.500000 3.000000
## 11 5.220153 5.000000 5.220153 1.500000 0.000000 1.500000
## 12 5.830952 5.220153 5.000000 3.000000 1.500000 0.000000
## 13 0.000000 1.500000 3.000000 5.000000 5.220153 5.830952
## 14 1.500000 0.000000 1.500000 5.220153 5.000000 5.220153
## 15 3.000000 1.500000 0.000000 5.830952 5.220153 5.000000
## 16 5.000000 5.220153 5.830952 0.000000 1.500000 3.000000
## 17 5.220153 5.000000 5.220153 1.500000 0.000000 1.500000
## 18 5.830952 5.220153 5.000000 3.000000 1.500000 0.000000
## 19 0.000000 1.500000 3.000000 5.000000 5.220153 5.830952
## 20 1.500000 0.000000 1.500000 5.220153 5.000000 5.220153
## 21 3.000000 1.500000 0.000000 5.830952 5.220153 5.000000
## 22 5.000000 5.220153 5.830952 0.000000 1.500000 3.000000
## 23 5.220153 5.000000 5.220153 1.500000 0.000000 1.500000
## 24 5.830952 5.220153 5.000000 3.000000 1.500000 0.000000matDistT## 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22
## 1 0 0 0 0 0 0 1 1 1 1 1 1 2 2 2 2 2 2 3 3 3 3
## 2 0 0 0 0 0 0 1 1 1 1 1 1 2 2 2 2 2 2 3 3 3 3
## 3 0 0 0 0 0 0 1 1 1 1 1 1 2 2 2 2 2 2 3 3 3 3
## 4 0 0 0 0 0 0 1 1 1 1 1 1 2 2 2 2 2 2 3 3 3 3
## 5 0 0 0 0 0 0 1 1 1 1 1 1 2 2 2 2 2 2 3 3 3 3
## 6 0 0 0 0 0 0 1 1 1 1 1 1 2 2 2 2 2 2 3 3 3 3
## 7 1 1 1 1 1 1 0 0 0 0 0 0 1 1 1 1 1 1 2 2 2 2
## 8 1 1 1 1 1 1 0 0 0 0 0 0 1 1 1 1 1 1 2 2 2 2
## 9 1 1 1 1 1 1 0 0 0 0 0 0 1 1 1 1 1 1 2 2 2 2
## 10 1 1 1 1 1 1 0 0 0 0 0 0 1 1 1 1 1 1 2 2 2 2
## 11 1 1 1 1 1 1 0 0 0 0 0 0 1 1 1 1 1 1 2 2 2 2
## 12 1 1 1 1 1 1 0 0 0 0 0 0 1 1 1 1 1 1 2 2 2 2
## 13 2 2 2 2 2 2 1 1 1 1 1 1 0 0 0 0 0 0 1 1 1 1
## 14 2 2 2 2 2 2 1 1 1 1 1 1 0 0 0 0 0 0 1 1 1 1
## 15 2 2 2 2 2 2 1 1 1 1 1 1 0 0 0 0 0 0 1 1 1 1
## 16 2 2 2 2 2 2 1 1 1 1 1 1 0 0 0 0 0 0 1 1 1 1
## 17 2 2 2 2 2 2 1 1 1 1 1 1 0 0 0 0 0 0 1 1 1 1
## 18 2 2 2 2 2 2 1 1 1 1 1 1 0 0 0 0 0 0 1 1 1 1
## 19 3 3 3 3 3 3 2 2 2 2 2 2 1 1 1 1 1 1 0 0 0 0
## 20 3 3 3 3 3 3 2 2 2 2 2 2 1 1 1 1 1 1 0 0 0 0
## 21 3 3 3 3 3 3 2 2 2 2 2 2 1 1 1 1 1 1 0 0 0 0
## 22 3 3 3 3 3 3 2 2 2 2 2 2 1 1 1 1 1 1 0 0 0 0
## 23 3 3 3 3 3 3 2 2 2 2 2 2 1 1 1 1 1 1 0 0 0 0
## 24 3 3 3 3 3 3 2 2 2 2 2 2 1 1 1 1 1 1 0 0 0 0
## 23 24
## 1 3 3
## 2 3 3
## 3 3 3
## 4 3 3
## 5 3 3
## 6 3 3
## 7 2 2
## 8 2 2
## 9 2 2
## 10 2 2
## 11 2 2
## 12 2 2
## 13 1 1
## 14 1 1
## 15 1 1
## 16 1 1
## 17 1 1
## 18 1 1
## 19 0 0
## 20 0 0
## 21 0 0
## 22 0 0
## 23 0 0
## 24 0 0sigma## 1
## 1 0.0224999999999999991673327315311325946822762489318847656250000
## 2 0.0000066776797753472399274865707596848807270362158305943012238
## 3 0.0000000000000001745640467031612522788968514235007086808448520
## 4 0.0000000000000000000000000000000000000000143583827581367797582
## 5 0.0000000000000000000000000000000000000000000042613636511423543
## 6 0.0000000000000000000000000000000000000000000000000000001113981
## 7 0.0057840616966580975927270102943111851345747709274291992187500
## 8 0.0007168131149851337830664066430585990019608289003372192382812
## 9 0.0000013643475657859583439243233299320579021696175914257764816
## 10 0.0000000000004857106754824595982789570016222239747178193725041
## 11 0.0000000000000601936494687245644879201301829867522713872138307
## 12 0.0000000000000001145696938456985277283312171491699972437340957
## 13 0.0017914012738853503543812184517491914448328316211700439453125
## 14 0.0009382885903262112121600568848123202769784256815910339355469
## 15 0.0001348239681125494701576655875996380018477793782949447631836
## 16 0.0000013569558875775789074329515451755590049742750125005841255
## 17 0.0000007107375915439390617206211891998535179482132662087678909
## 18 0.0000001021268545377872649108357970722249508099821468931622803
## 19 0.0008330248056275453864480406984682758775306865572929382324219
## 20 0.0006166745823446492802411000866413814947009086608886718750000
## 21 0.0002501787346616134882250348514531879118294455111026763916016
## 22 0.0000294798909060135976912316729814378390983620192855596542358
## 23 0.0000218234790719545488843489344787940353853628039360046386719
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## 24 0.0224999999999999991673327315311325946822762489318847656250000datos1## x y t z((x,y),t)
## 1 0.0 1 1 -0.197111293
## 2 1.5 1 1 0.032270503
## 3 3.0 1 1 0.199972606
## 4 0.0 6 1 -0.165773804
## 5 1.5 6 1 -0.134474031
## 6 3.0 6 1 -0.020170152
## 7 0.0 1 2 -0.093278873
## 8 1.5 1 2 0.052621834
## 9 3.0 1 2 0.298552274
## 10 0.0 6 2 -0.059641380
## 11 1.5 6 2 -0.028833549
## 12 3.0 6 2 0.024173647
## 13 0.0 1 3 -0.042869743
## 14 1.5 1 3 -0.193806283
## 15 3.0 1 3 -0.058370448
## 16 0.0 6 3 -0.023235489
## 17 1.5 6 3 -0.116042993
## 18 3.0 6 3 -0.037479098
## 19 0.0 1 4 0.006021199
## 20 1.5 1 4 -0.337476441
## 21 3.0 1 4 0.051772796
## 22 0.0 6 4 -0.085509049
## 23 1.5 6 4 -0.045540092
## 24 3.0 6 4 -0.058455223- Se requiere predecir predecir en el tiempo \(t=2.3\) y en el lugar \(s_0=(1.5,2.7)\). Nótese que tanto el dominio espacial como el dominio temporal con continuos y fijos. A continuación se presenta el procedimiento para llevar a cabo Kriging simple con su respectiva varianza de error de predicción estimada
grillaSpT0=rbind(expand.grid(x1,x2,t),c(1.5,2.7,2.3))
matDistSp0=as.matrix(dist(grillaSpT0[,1:2]))
matDistT0=as.matrix(dist(grillaSpT0[,3:3]))
sigma0=cressie1(matDistSp0,matDistT0,p=c(0.15,1.7,1.9))
#vector de covarianzas entre la coordenada a predecir y las observadas
sigma0## 1
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## 6 -0.00003276782
## 7 -0.00421288727
## 8 -0.01073643525
## 9 -0.00421288727
## 10 -0.00005666790
## 11 -0.00009187561
## 12 -0.00005666790
## 13 -0.00554359594
## 14 -0.00485786885
## 15 -0.00554359594
## 16 -0.00022122643
## 17 -0.00045970408
## 18 -0.00022122643
## 19 0.01587928193
## 20 0.03629635060
## 21 0.01587928193
## 22 0.00070649170
## 23 0.00168519595
## 24 0.00070649170z_pred0=t(lambda)%*%datos1[,4]
z_pred0## [,1]
## [1,] -0.01036865VarErropred0=sigma[1,1]-t(sigma0[25,-25])%*%solve(sigma)%*%sigma0[25,-25]
VarErropred0## [,1]
## [1,] 0.02243925.3 Algunas funciones de covarianza espacio temporal no separables
##Funciones de covarianza espacio temporal p vector de parámetros para cada modelo
exp_esp_temp=function(h,u,p){((p[1])^2)*exp(-h/p[2]-u/p[3])}
gauss_esp_temp=function(h,u,p){(p[1]^2)*exp(-(h/p[2])^2-(u/p[3])^2)}
cressie1=function(h,u,p){(p[1]^2/((p[2]^2*u^2+1)))*exp(-(p[3]^2*h^2)/(p[2]^2*u^2+1))}
Gneiting1=function(h,u,p){p[1]^2/((p[2]*u^(2*p[3])+1)^(p[4]))*exp(-(p[6]*h^(2*p[5]))/((p[2]*u^(2*p[3])+1)^(p[4]*p[5])))}
Gneiting2=function(h,u,sigma,p)
{p[1]^2/((2^(p[3]-1))*p[7](p[3])*(p[2]*u^(2*p[3])+1)^(p[4]+p[5]))*
(((p[6]*h)/((p[2]*u^(2*p[3])+1)^(p[5]/2)))^p[3])*
besselK(((p[6]*h)/((p[2]*u^(2*p[3])+1)^(p[5]/2))),p[3])}
Iaco_Cesare=function(h,u,a,b,c){(1+h^p[1]+u^p[2])^(-p[3])}5.3.1 C R E S S I E - H U A N G (1999)
#sigma:desviacion estandar, a es el parámetros de escala del tiempo, b es el parámetros de escala del espacio, d es la dimensión espacial; a,b positivos
CH_1=function(h,u,p,d){(p[1]^2/((p[2]^2*u^2+1)^(d/2)))*exp(-(p[3]^2*h^2)/(p[2]^2*u^2+1))}
CH_2=function(h,u,p,d){(p[1]^2/((p[2]*abs(u)+1)^(d/2)))*exp(-(p[3]^2*h^2)/(p[2]*abs(u)+1))}
CH_3=function(h,u,p,d){p[1]^2*((p[2]^2)*(u^2)+1)/(((p[2]^2)*(u^2)+1)^2+(p[3]^2)*h^2)^((d+1)/2)}
CH_4=function(h,u,p,d){p[1]^2*(p[2]*abs(u)+1)/((p[2]*abs(u)+1)^2+(p[3]^2)*h^2)^((d+1)/2)}
#el caso mas general de C R E S S I E - H U A N G (1999) es cuando d=2, entonces queda
CH_1=function(h,u,p){(p[1]^2/((p[2]^2*u^2+1)))*exp(-(p[3]^2*h^2)/(p[2]^2*u^2+1))}
CH_2=function(h,u,p){(p[1]^2/((p[2]*abs(u)+1)))*exp(-(p[3]^2*h^2)/(p[2]*abs(u)+1))}
CH_3=function(h,u,p){p[1]^2*((p[2]^2)*(u^2)+1)/(((p[2]^2)*(u^2)+1)^2+(p[3]^2)*h^2)^((3)/2)}
CH_4=function(h,u,p){p[1]^2*(p[2]*abs(u)+1)/((p[2]*abs(u)+1)^2+(p[3]^2)*h^2)^((3)/2)}5.3.2 Gneiting (2002), combina fun1, fun2 y psi en Gneiting
#fun1
phi1=function(r,c,gama,v){v*exp(-c*r^gama)} #c>0, 0<gama<=1, siempre v=1
phi2=function(r,c,gama,v){((2^(v-1))*gamma(v))^(-1)*(c*r^0.5)^v*besselK(c*r^0.5,v)} #c>0, v>0
phi3=function(r,c,gama,v){(1+c*r^gama)^(-v)} #c>0, 0<gama<=1, v>0
phi4=function(r,c,gama,v){gama*(2^v)*(exp(c*r^0.5)+exp(-c*r^0.5))^(-v)} #c>0, v>0, siempre gama=1
#fun2
psi1=function(r,a,alpha,beta){(a*r^alpha+1)^beta} #a>0, 0<alpha<=1, 0<=beta<=1
psi2=function(r,a,alpha,beta){log(a*r^alpha+beta)/log(beta)} #a>0, beta>1, 0<alpha<=1
psi3=function(r,a,alpha,beta){(a*r^alpha+beta)/(beta*(a*r^alpha+1))} #a>0, 0<beta<=1 0<alpha<=1
#Cualquier combinación genera una función de covarianza válida
Gneiting=function(h,u,sigma,d,a,alpha,beta,c,gama,v,psi,phi){(sigma^2/(psi((abs(u)^2),a,alpha,beta))^(d/2))*phi(h^2/(psi(abs(u)^2,a,alpha,beta)),c,gama,v)}
#el caso mas general de Gneiting (2002) es cuando d=2, entonces queda
Gneiting=function(h,u,sigma,a,alpha,beta,c,gama,v,psi,phi){(sigma^2/(psi((abs(u)^2),a,alpha,beta)))*phi(h^2/(psi(abs(u)^2,a,alpha,beta)),c,gama,v)}####IACO_CESSARE
C_IACO_CESSARE=function(h,u,sigma,a,b,alpha,beta,gama){(1 + (h/a)^alpha + (u/b)^beta)^(-gama)}#(Porcu, 2007) Basado en la función de supervivencia de Dagum
#función de Dagum
Dagum=function(r,lambda,theta,epsilon){1-1/(1+lambda*r^(-theta))^epsilon} #lamdba, theta in (0,7), epsilon in (0,7)
Dagumm=function(r,lambda,theta,epsilon){ifelse(r==0,1,Dagum(r,lambda,theta,epsilon))}
Porcu_sep=function(h,u,lambda_h,theta_h,epsilon_h,lambda_u,theta_u,epsilon_u){Dagumm(h,lambda_h,theta_h,epsilon_h)*Dagumm(u,lambda_u,theta_u,epsilon_u)}
Porcu_Nsep=function(h,u,lambda_h,theta_h,epsilon_h,lambda_u,theta_u,epsilon_u,vartheta){vartheta*Dagumm(h,lambda_h,theta_h,epsilon_h)+(1-vartheta)*Dagumm(u,lambda_u,theta_u,epsilon_u)}6 Pulimiento de medianas
Esta es una alternativa al modelamiento de la media cuando los modelos de regresión polinómicos usuales no logran el objetivo de eliminar la tendencia ya sea porque el tipo de tendencia corresponde mas a unas ventanas móviles o porque hay presentes datos atípicos.
6.1 Cargar librerias
Lista de librerías con link a la documentación.
library(gstat)
library(sp)
library(mvtnorm)6.2 Grilla de las ubicaciones espaciales.
n_x <- 4
n_y <- 6
x <- seq(0, 1, len = n_x)
y <- seq(0, 1, len = n_y)
coordenadas <- as.data.frame(expand.grid(x, y))
names(coordenadas) <- c("X", "Y")Encabezado coordenadas
| X | Y |
|---|---|
| 0.0000000 | 0.0 |
| 0.3333333 | 0.0 |
| 0.6666667 | 0.0 |
| 1.0000000 | 0.0 |
| 0.0000000 | 0.2 |
| 0.3333333 | 0.2 |
6.3 Definición de objeto VGM
Esto define un objeto vgm que es el tipo de objeto que usa el paquete gstat para los modelos teóricos de variograma. Con este objeto se pueden definir modelos anidados.
vario <- vgm(10, # Punto de silla
"Exp", # Modelo, ver documentación
0.5) # Rango
print(vario)## model psill range
## 1 Exp 10 0.56.4 Matriz de varianza dadas coordenadas.
coordinates(coordenadas) <- ~X + Y
class(coordenadas) # Cambio de objedto dataframe a sp## [1] "SpatialPoints"
## attr(,"package")
## [1] "sp"cov_mat <- vgmArea(coordenadas, # Matriz de ubiaciones SP
vgm = vario) # VGM object
print(dim(cov_mat))## [1] 24 246.5 Simulación.
Simulación dada la media y la matriz de varianza
mu <- rep(0, n_x * n_y) # Media del proceso
simu <- rmvnorm(1,
mean = mu,
sigma = cov_mat)
print(simu[1:5])## [1] -2.5513037 0.9276826 -3.6661586 -0.6549925 -1.19385766.6 Pulimiento de medianas
Unir las coordenadas con la columna de simulación
data <- as.data.frame(cbind(coordenadas@coords,
Simula = t(simu)))
names(data) <- c("X", "Y", "Var")
print(head(data))## X Y Var
## 1 0.0000000 0.0 -2.5513037
## 2 0.3333333 0.0 0.9276826
## 3 0.6666667 0.0 -3.6661586
## 4 1.0000000 0.0 -0.6549925
## 5 0.0000000 0.2 -1.1938576
## 6 0.3333333 0.2 -2.7590614Reshape para matriz, esto transforma la tabla de datos en matriz
tabla <- reshape2::dcast(data,
X ~ Y,
value.var = "Var")
rownames(tabla) <- tabla[, 1]
tabla <- tabla[, c(-1)]
print(tabla)## 0 0.2 0.4 0.6
## 0 -2.5513037 -1.193858 3.6188035 2.0630539
## 0.333333333333333 0.9276826 -2.759061 -1.0523709 4.8051856
## 0.666666666666667 -3.6661586 -3.658275 -0.8451633 0.2559103
## 1 -0.6549925 -1.863424 -7.3200303 -4.7032245
## 0.8 1
## 0 3.085683 7.8949942
## 0.333333333333333 4.220137 1.5338289
## 0.666666666666667 1.432050 -0.4119245
## 1 -4.584308 -1.2695238Pulimiento de medianas de la tabla
med <- medpolish(tabla)## 1: 42.82888
## 2: 41.35189
## Final: 41.35189geo_data <- reshape2::melt(med$residuals)
print(med)##
## Median Polish Results (Dataset: "tabla")
##
## Overall: 0.08855764
##
## Row Effects:
## 0 0.333333333333333 0.666666666666667
## 1.1901479 0.9456328 -0.9456328
## 1
## -4.5026503
##
## Column Effects:
## 0 0.2 0.4 0.6 0.8
## -1.4577956 -2.6368817 -1.0373247 0.9486669 2.0480517
## 1
## 1.8221036
##
## Residuals:
## 0 0.2 0.4 0.6 0.8
## 0 -2.3722 0.16432 3.3774 -0.16432 -0.24107
## 0.333333333333333 1.3513 -1.15637 -1.0492 2.82233 1.13789
## 0.666666666666667 -1.3513 -0.16432 1.0492 0.16432 0.24107
## 1 5.2169 5.18755 -1.8686 -1.23780 -2.21827
## 1
## 0 4.7942
## 0.333333333333333 -1.3225
## 0.666666666666667 -1.3770
## 1 1.3225Reshape de los datos, con efecto de la fila y la columna
tabla_residuales <- as.data.frame(med$residuals)
names(tabla_residuales) <- med$col
rownames(tabla_residuales) <- med$row
geo_data <- reshape2::melt(as.matrix(tabla_residuales))
geo_data <- cbind(data,
geo_data,
med$overall)
names(geo_data) <- c("X",
"Y",
"Var",
"Efecto fila",
"Efecto columa",
"Residual",
"Efecto Global")
print(geo_data)## X Y Var Efecto fila Efecto columa
## 1 0.0000000 0.0 -2.5513037 1.1901479 -1.4577956
## 2 0.3333333 0.0 0.9276826 0.9456328 -1.4577956
## 3 0.6666667 0.0 -3.6661586 -0.9456328 -1.4577956
## 4 1.0000000 0.0 -0.6549925 -4.5026503 -1.4577956
## 5 0.0000000 0.2 -1.1938576 1.1901479 -2.6368817
## 6 0.3333333 0.2 -2.7590614 0.9456328 -2.6368817
## 7 0.6666667 0.2 -3.6582755 -0.9456328 -2.6368817
## 8 1.0000000 0.2 -1.8634239 -4.5026503 -2.6368817
## 9 0.0000000 0.4 3.6188035 1.1901479 -1.0373247
## 10 0.3333333 0.4 -1.0523709 0.9456328 -1.0373247
## 11 0.6666667 0.4 -0.8451633 -0.9456328 -1.0373247
## 12 1.0000000 0.4 -7.3200303 -4.5026503 -1.0373247
## 13 0.0000000 0.6 2.0630539 1.1901479 0.9486669
## 14 0.3333333 0.6 4.8051856 0.9456328 0.9486669
## 15 0.6666667 0.6 0.2559103 -0.9456328 0.9486669
## 16 1.0000000 0.6 -4.7032245 -4.5026503 0.9486669
## 17 0.0000000 0.8 3.0856834 1.1901479 2.0480517
## 18 0.3333333 0.8 4.2201366 0.9456328 2.0480517
## 19 0.6666667 0.8 1.4320504 -0.9456328 2.0480517
## 20 1.0000000 0.8 -4.5843084 -4.5026503 2.0480517
## 21 0.0000000 1.0 7.8949942 1.1901479 1.8221036
## 22 0.3333333 1.0 1.5338289 0.9456328 1.8221036
## 23 0.6666667 1.0 -0.4119245 -0.9456328 1.8221036
## 24 1.0000000 1.0 -1.2695238 -4.5026503 1.8221036
## Residual Efecto Global
## 1 -2.3722137 0.08855764
## 2 1.3512877 0.08855764
## 3 -1.3512877 0.08855764
## 4 5.2168958 0.08855764
## 5 0.1643186 0.08855764
## 6 -1.1563701 0.08855764
## 7 -0.1643186 0.08855764
## 8 5.1875505 0.08855764
## 9 3.3774227 0.08855764
## 10 -1.0492366 0.08855764
## 11 1.0492366 0.08855764
## 12 -1.8686129 0.08855764
## 13 -0.1643186 0.08855764
## 14 2.8223282 0.08855764
## 15 0.1643186 0.08855764
## 16 -1.2377987 0.08855764
## 17 -0.2410739 0.08855764
## 18 1.1378945 0.08855764
## 19 0.2410739 0.08855764
## 20 -2.2182674 0.08855764
## 21 4.7941850 0.08855764
## 22 -1.3224652 0.08855764
## 23 -1.3769530 0.08855764
## 24 1.3224652 0.08855764Validación de la descomposición
valida <- cbind(geo_data$Var,
geo_data[["Efecto fila"]] +
geo_data[["Efecto columa"]] +
geo_data[["Residual"]] +
geo_data[["Efecto Global"]])
valida <- as.data.frame(valida)
names(valida) <- c("datos", "suma")
print(valida)## datos suma
## 1 -2.5513037 -2.5513037
## 2 0.9276826 0.9276826
## 3 -3.6661586 -3.6661586
## 4 -0.6549925 -0.6549925
## 5 -1.1938576 -1.1938576
## 6 -2.7590614 -2.7590614
## 7 -3.6582755 -3.6582755
## 8 -1.8634239 -1.8634239
## 9 3.6188035 3.6188035
## 10 -1.0523709 -1.0523709
## 11 -0.8451633 -0.8451633
## 12 -7.3200303 -7.3200303
## 13 2.0630539 2.0630539
## 14 4.8051856 4.8051856
## 15 0.2559103 0.2559103
## 16 -4.7032245 -4.7032245
## 17 3.0856834 3.0856834
## 18 4.2201366 4.2201366
## 19 1.4320504 1.4320504
## 20 -4.5843084 -4.5843084
## 21 7.8949942 7.8949942
## 22 1.5338289 1.5338289
## 23 -0.4119245 -0.4119245
## 24 -1.2695238 -1.26952387 Introducción proceso espacial bivariado
Martha Bohorquez
19/5/2022
7.2 Ubicaciones: En este caso se supone que ambos procesos están observados en los mismos lugares
x=seq(0,1,len=3)
y=seq(0,1,len=4)
coordenadas=expand.grid(x,y)
Mat_dist=as.matrix(dist(coordenadas))7.3 Modelo lineal de coregionalización
Cova1=function(h,a){exp(-h/a)}
Cova2=function(h,a){ifelse(h <= a, 1-1.5*(h/a)+0.5*(h/a)^3, 0)}
B1=matrix(c(26.3,0.3,0.3,2.1),nrow=2,byrow=T)
B2=matrix(c(2.1,1.3,1.3,17.5),nrow=2,byrow=T)
Mat_Cov_bloque11=B1[1,1]*Cova1(Mat_dist,1)+B2[1,1]*Cova2(Mat_dist,0.5)
Mat_Cov_bloque22=B1[2,2]*Cova1(Mat_dist,1)+B2[2,2]*Cova2(Mat_dist,0.5)
Mat_Cov_bloque12=B1[1,2]*Cova1(Mat_dist,1)+B2[1,2]*Cova2(Mat_dist,0.5)
Mat_Cov_bloque21=B1[2,1]*Cova1(Mat_dist,1)+B2[2,1]*Cova2(Mat_dist,0.5)
MAT_COV=rbind(cbind(Mat_Cov_bloque11,Mat_Cov_bloque12),cbind(Mat_Cov_bloque21,Mat_Cov_bloque22))
dim(MAT_COV)## [1] 24 24det(MAT_COV)## [1] 3494165764254141523417177784328 Geoestadística con sgeostat
8.1 Data Load
aquifer=read.table("data/aquifer.txt",head=T,dec=",")
head(aquifer)## Este Norte Profundidad
## 1 42.78275 127.62282 1464
## 2 -27.39691 90.78732 2553
## 3 -1.16289 84.89600 2158
## 4 -18.61823 76.45199 2455
## 5 96.46549 64.58058 1756
## 6 108.56243 82.92325 17028.3 Including Plots
g1=ggplot(aquifer, aes(Profundidad, Este)) +
geom_point() +
geom_line() +
xlab("Este") +
ylab("Profundidad")
g2=ggplot(aquifer, aes(Profundidad, Norte)) +
geom_point() +
geom_line() +
xlab("Norte") +
ylab("Profundidad")
g3=ggplot(aquifer, aes(Profundidad, Este*Norte)) +
geom_point() +
geom_line() +
xlab("Interacción este,norte") +
ylab("Profundidad")
plot_grid(g1,g2,g3)
cor(aquifer)## Este Norte Profundidad
## Este 1.0000000 0.1147565 -0.7788885
## Norte 0.1147565 1.0000000 -0.6200923
## Profundidad -0.7788885 -0.6200923 1.0000000scatterplot3d(aquifer, highlight.3d=TRUE, col.axis="blue",
col.grid="lightblue", main="Tendencia de Profundidad", pch=20)
reg1 <- lm(Profundidad ~ Este + Norte, data = aquifer)
residuales1 <- residuals(reg1)
summary(reg1)##
## Call:
## lm(formula = Profundidad ~ Este + Norte, data = aquifer)
##
## Residuals:
## Min 1Q Median 3Q Max
## -366.96 -161.53 -30.71 148.15 651.20
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2591.4302 38.9599 66.52 <0.0000000000000002
## Este -6.7514 0.3438 -19.64 <0.0000000000000002
## Norte -5.9872 0.4066 -14.73 <0.0000000000000002
##
## (Intercept) ***
## Este ***
## Norte ***
## ---
## Signif. codes:
## 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 203.3 on 82 degrees of freedom
## Multiple R-squared: 0.8921, Adjusted R-squared: 0.8894
## F-statistic: 338.9 on 2 and 82 DF, p-value: < 0.00000000000000022anova(reg1)## Analysis of Variance Table
##
## Response: Profundidad
## Df Sum Sq Mean Sq F value Pr(>F)
## Este 1 19045642 19045642 460.95 < 0.00000000000000022
## Norte 1 8960172 8960172 216.86 < 0.00000000000000022
## Residuals 82 3388069 41318
##
## Este ***
## Norte ***
## Residuals
## ---
## Signif. codes:
## 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1reg2 <- lm(Profundidad ~ Este*Norte, data = aquifer)
residuales2 <- residuals(reg2)
summary(reg2)##
## Call:
## lm(formula = Profundidad ~ Este * Norte, data = aquifer)
##
## Residuals:
## Min 1Q Median 3Q Max
## -406.30 -138.88 -13.04 129.36 722.48
##
## Coefficients:
## Estimate Std. Error t value
## (Intercept) 2627.069474 38.325720 68.546
## Este -8.287218 0.565845 -14.646
## Norte -6.648559 0.432667 -15.366
## Este:Norte 0.024524 0.007401 3.314
## Pr(>|t|)
## (Intercept) < 0.0000000000000002 ***
## Este < 0.0000000000000002 ***
## Norte < 0.0000000000000002 ***
## Este:Norte 0.00138 **
## ---
## Signif. codes:
## 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 191.9 on 81 degrees of freedom
## Multiple R-squared: 0.905, Adjusted R-squared: 0.9014
## F-statistic: 257.1 on 3 and 81 DF, p-value: < 0.00000000000000022anova(reg2)## Analysis of Variance Table
##
## Response: Profundidad
## Df Sum Sq Mean Sq F value
## Este 1 19045642 19045642 517.06
## Norte 1 8960172 8960172 243.25
## Este:Norte 1 404448 404448 10.98
## Residuals 81 2983621 36835
## Pr(>F)
## Este < 0.00000000000000022 ***
## Norte < 0.00000000000000022 ***
## Este:Norte 0.001379 **
## Residuals
## ---
## Signif. codes:
## 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1reg3 <- lm(Profundidad ~ Este*Norte+I(Este^2)*I(Norte^2), data = aquifer)
residuales3 <- residuals(reg3)
summary(reg3)##
## Call:
## lm(formula = Profundidad ~ Este * Norte + I(Este^2) * I(Norte^2),
## data = aquifer)
##
## Residuals:
## Min 1Q Median 3Q Max
## -372.7 -133.6 -20.3 129.9 505.1
##
## Coefficients:
## Estimate Std. Error t value
## (Intercept) 2537.5624340948 70.3799189709 36.055
## Este -7.7283066535 0.6027554102 -12.822
## Norte -3.0747325957 1.7697466886 -1.737
## I(Este^2) -0.0067922127 0.0059674654 -1.138
## I(Norte^2) -0.0237215094 0.0090487081 -2.622
## Este:Norte 0.0115491188 0.0096804349 1.193
## I(Este^2):I(Norte^2) 0.0000022515 0.0000009541 2.360
## Pr(>|t|)
## (Intercept) <0.0000000000000002 ***
## Este <0.0000000000000002 ***
## Norte 0.0863 .
## I(Este^2) 0.2585
## I(Norte^2) 0.0105 *
## Este:Norte 0.2365
## I(Este^2):I(Norte^2) 0.0208 *
## ---
## Signif. codes:
## 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 180.7 on 78 degrees of freedom
## Multiple R-squared: 0.9189, Adjusted R-squared: 0.9126
## F-statistic: 147.2 on 6 and 78 DF, p-value: < 0.00000000000000022anova(reg3)## Analysis of Variance Table
##
## Response: Profundidad
## Df Sum Sq Mean Sq F value
## Este 1 19045642 19045642 583.2335
## Norte 1 8960172 8960172 274.3868
## I(Este^2) 1 55368 55368 1.6955
## I(Norte^2) 1 152170 152170 4.6599
## Este:Norte 1 451567 451567 13.8283
## I(Este^2):I(Norte^2) 1 181854 181854 5.5689
## Residuals 78 2547110 32655
## Pr(>F)
## Este < 0.00000000000000022 ***
## Norte < 0.00000000000000022 ***
## I(Este^2) 0.1967061
## I(Norte^2) 0.0339500 *
## Este:Norte 0.0003755 ***
## I(Este^2):I(Norte^2) 0.0207829 *
## Residuals
## ---
## Signif. codes:
## 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1aquifer=data.frame(aquifer,resi=residuales2)
aquifer_points=point(aquifer, x="Este", y="Norte")
aquifer_pair=pair(aquifer_points,num.lags=10)## ....................................................................................aquifer_pair$bins## [1] 13.55308 40.65923 67.76539 94.87154 121.97770
## [6] 149.08385 176.19001 203.29616 230.40231 257.50847aquifer_pair$dist## [1] 79.259313 61.292744 79.928307 82.801936 79.529981
## [6] 84.514408 100.208558 107.152008 89.978304 104.178541
## [11] 99.251058 88.899718 87.945051 70.165987 101.674210
## [16] 112.872165 120.961308 119.047906 32.754634 46.156920
## [21] 27.689647 74.010375 65.729277 107.885946 23.229828
## [26] 87.355532 98.880862 107.581460 104.100879 104.150438
## [31] 52.285133 71.583372 76.011219 87.033342 51.194751
## [36] 129.805262 135.555137 122.851465 125.340545 49.219772
## [41] 119.707807 119.905108 123.155773 112.001822 114.916408
## [46] 115.460198 103.829256 104.179897 113.250471 96.543519
## [51] 97.566287 96.700258 82.781495 63.156546 64.218322
## [56] 65.835477 24.567616 35.106924 54.832521 45.809186
## [61] 40.330280 56.110555 43.935695 46.519216 45.713177
## [66] 50.431563 50.801512 61.124807 55.902846 44.604704
## [71] 62.449544 185.852432 212.770561 123.323713 143.256052
## [76] 141.135610 169.641608 148.183229 143.187705 166.176744
## [81] 149.417056 150.251941 166.077707 163.208576 26.887385
## [86] 16.809727 126.604452 136.186584 120.744768 128.246553
## [91] 133.677383 129.683492 130.511843 129.585165 130.769649
## [96] 94.037999 23.325651 105.307950 123.522448 133.049760
## [101] 131.853495 97.723076 103.926618 93.928059 79.959358
## [106] 72.440973 147.319592 99.601194 54.101819 55.632916
## [111] 65.873035 62.225650 62.421578 91.321524 85.948043
## [116] 81.564157 68.656804 129.954829 75.968082 81.463104
## [121] 69.079720 74.315712 101.967004 145.128267 145.470767
## [126] 148.443085 60.943426 61.309844 61.953184 55.477879
## [131] 53.875066 81.957351 106.216568 112.476289 109.958325
## [136] 60.835750 47.647137 41.488835 46.622184 68.602648
## [141] 50.302378 25.536379 116.404782 113.601262 129.467598
## [146] 121.021665 123.665659 117.773861 122.244383 123.329873
## [151] 35.035312 47.569309 123.256491 138.745457 109.244082
## [156] 133.512160 46.681150 67.213847 63.044705 93.401359
## [161] 69.021050 65.844134 87.119306 71.711292 71.623479
## [166] 87.607834 85.955074 19.390467 99.719691 109.743053
## [171] 93.935947 101.986099 107.639797 102.835886 104.438025
## [176] 103.169612 103.891523 102.463199 38.358960 81.664216
## [181] 99.316764 108.881593 107.535211 73.645102 78.352029
## [186] 70.404750 54.443063 46.299248 120.568893 83.851048
## [191] 37.288803 44.569863 54.995234 51.090048 51.224206
## [196] 64.612945 90.728452 88.827991 82.592611 112.322576
## [201] 72.855185 78.735670 65.600016 69.384909 95.432264
## [206] 119.389544 119.721763 122.770574 55.218671 57.286526
## [211] 57.902693 47.558372 47.088151 67.393203 81.542159
## [216] 87.260250 84.885977 74.954007 55.993465 51.066520
## [221] 56.378090 58.765641 42.864537 23.977824 103.963732
## [226] 99.820726 115.962930 105.087557 107.699134 104.691742
## [231] 109.393102 110.147836 8.935570 20.810342 102.759122
## [236] 116.226434 124.934060 154.892599 72.895198 93.334966
## [241] 88.068221 119.167718 90.187266 82.934575 107.549563
## [246] 89.306141 91.020385 106.441436 102.684866 115.694395
## [251] 127.345190 108.834938 114.849692 119.917484 117.966887
## [256] 116.818490 116.460383 119.367633 108.451356 38.352281
## [261] 89.833391 108.237636 117.699999 116.595192 92.896467
## [266] 97.006166 89.746654 66.086035 59.478867 135.007450
## [271] 102.002272 37.463975 38.972587 49.341747 45.626279
## [276] 45.816907 81.899220 98.972448 95.465680 84.467758
## [281] 131.106894 61.508958 67.219814 54.379847 59.229277
## [286] 109.962937 130.949665 131.302206 134.179409 45.391386
## [291] 46.273339 46.922209 39.289389 37.894974 65.177065
## [296] 91.335167 97.965398 95.345994 76.615804 61.339143
## [301] 55.438231 60.800160 74.339658 56.837840 32.970465
## [306] 121.092218 117.412471 133.534215 123.397383 126.028178
## [311] 122.060727 126.701758 127.579674 24.388090 36.877600
## [316] 122.044937 135.607864 105.937898 135.563755 56.560643
## [321] 76.542772 70.232074 101.732211 70.933202 63.620474
## [326] 88.187946 69.968883 71.632746 87.060671 83.467540
## [331] 21.972471 11.475671 26.124366 31.693577 8.380367
## [336] 30.070646 23.161115 6.209140 170.214009 132.147156
## [341] 55.124664 51.353913 54.430899 52.534299 51.273236
## [346] 37.275273 55.886912 54.189985 57.445879 25.084164
## [351] 93.328281 91.783938 103.143550 104.608208 103.503813
## [356] 103.379914 36.435484 154.009131 157.641397 164.508297
## [361] 95.468867 128.230331 132.100422 124.079663 122.594467
## [366] 129.038237 41.839840 41.896069 44.757880 115.677434
## [371] 119.651450 119.827187 109.589713 111.574801 96.407188
## [376] 47.008541 40.863332 42.707944 158.664674 137.180819
## [381] 135.610055 139.227500 106.066768 108.434174 113.351195
## [386] 113.851492 106.757833 115.974365 100.119280 101.167428
## [391] 111.758515 115.045274 114.135715 91.989485 79.260339
## [396] 76.004414 67.998656 205.317510 244.451025 172.056190
## [401] 192.215708 185.711843 217.327924 182.775827 170.615069
## [406] 197.830933 176.903637 181.060655 194.223065 187.354360
## [411] 33.296292 47.430350 52.185586 28.807239 51.092135
## [416] 44.174139 25.438238 167.220517 138.182432 76.668261
## [421] 73.234460 75.787614 73.948195 46.856865 34.717604
## [426] 51.958332 71.453225 72.567163 37.615554 84.619353
## [431] 108.114937 120.142473 122.822502 121.306658 121.204583
## [436] 45.467260 150.802242 155.528833 165.428365 80.320112
## [441] 146.986778 151.198855 142.329620 141.366327 121.195938
## [446] 60.430921 60.398169 62.804566 133.290441 137.236403
## [451] 137.475098 126.631757 128.429927 116.236335 68.515181
## [456] 62.705490 64.425905 160.345766 139.365571 138.762856
## [461] 141.704715 103.997489 110.021801 119.507637 102.435955
## [466] 95.493903 102.297808 87.028525 87.607833 99.959743
## [471] 102.615712 101.446172 103.006820 90.484265 61.319896
## [476] 49.232130 222.282477 259.668863 182.625380 203.078010
## [481] 197.510015 228.831590 196.671699 185.675987 212.538787
## [486] 192.069019 195.672024 209.541462 203.291640 17.277015
## [491] 23.884135 9.249078 21.491573 15.286287 11.450345
## [496] 170.601656 128.115646 43.656904 40.577200 44.579014
## [501] 42.618833 54.909465 41.310805 59.001264 45.056489
## [506] 49.596766 26.763715 97.524043 82.632041 93.555096
## [511] 94.402263 93.505930 93.371758 34.104112 154.626514
## [516] 157.659004 162.890952 102.794662 117.698059 121.410792
## [521] 113.788513 112.068493 132.291092 35.751337 35.899705
## [526] 39.065343 105.718715 109.690766 109.835396 99.942823
## [531] 102.011910 85.478726 35.550970 29.422107 31.233687
## [536] 156.692064 135.130369 133.066026 137.003184 106.655003
## [541] 107.065422 109.472270 119.095243 112.012274 122.341800
## [546] 106.370848 107.637851 117.219991 120.789057 120.020800
## [551] 85.776560 73.175783 83.406457 77.404167 195.448896
## [556] 235.323777 165.387896 185.318152 178.367342 210.034299
## [561] 174.400625 161.707476 189.023901 167.928111 172.341580
## [566] 185.133379 177.987519 6.945246 18.627690 4.217605
## [571] 3.538855 22.028562 184.915166 138.122730 35.972138
## [576] 26.539157 28.379003 26.522030 71.721980 58.352871
## [581] 75.597715 48.804976 55.807481 23.615308 114.306908
## [586] 84.398831 93.853821 92.744883 92.563786 92.399438
## [591] 48.358436 169.178814 171.715192 175.409523 120.055674
## [596] 114.439679 117.461202 111.484551 108.914153 148.583251
## [601] 19.577446 19.802596 23.079974 104.658509 108.556755
## [606] 108.600018 99.936292 102.205596 81.027208 29.044437
## [611] 21.176438 23.920446 168.876200 147.370281 144.793973
## [616] 149.046410 121.438341 120.220201 119.884679 136.150136
## [621] 129.078555 139.589827 123.613920 124.899192 134.327696
## [626] 137.950333 137.207183 93.339495 81.293693 100.653031
## [631] 93.983902 193.807825 235.546757 171.115952 190.506699
## [636] 182.770249 214.358016 176.713433 162.878229 190.250686
## [641] 168.884755 173.883827 185.690539 177.870735 23.640710
## [646] 3.249805 8.715944 26.852987 191.730323 144.155298
## [651] 37.413293 24.624456 24.175644 22.529215 78.578576
## [656] 65.132166 82.495350 53.853789 61.349535 23.267715
## [661] 121.179386 88.369829 97.255209 95.455133 95.537495
## [666] 95.363629 55.259820 176.026920 178.498974 181.936556
## [671] 126.455290 116.380751 119.107648 113.815178 110.930536
## [676] 155.519893 12.710986 12.956907 16.235144 107.498375
## [681] 111.344344 111.350044 103.186085 105.509780 82.764284
## [686] 31.481660 23.605644 26.465080 175.342914 153.863801
## [691] 151.190009 155.500722 128.323224 126.896457 126.040052
## [696] 142.935659 135.857963 146.206996 130.241022 131.487347
## [701] 141.084371 144.669825 143.904762 98.908472 87.058888
## [706] 107.020532 99.686568 196.099877 238.462396 175.954479
## [711] 195.150446 187.183444 218.698358 180.459255 166.266684
## [716] 193.596657 172.183164 177.373721 188.809522 180.764665
## [721] 22.317307 15.382003 3.437885 176.959530 136.512223
## [726] 50.739946 44.747769 46.981630 45.141200 58.988399
## [731] 45.024607 63.463361 54.279827 58.812042 18.601119
## [736] 101.287465 91.823868 102.650552 103.264654 102.464397
## [741] 102.326113 41.492546 160.841422 164.218445 170.301015
## [746] 103.849203 126.338500 129.922261 122.587236 120.718604
## [751] 136.781063 33.464363 33.518140 36.378738 114.682791
## [756] 118.651173 118.782931 109.017740 111.108731 93.795803
## [761] 42.831179 35.926540 38.124541 164.265416 142.723612
## [766] 140.877989 144.677025 112.840201 114.303436 117.796530
## [771] 122.044237 114.948290 124.313903 108.443027 109.511456
## [776] 119.985773 123.315227 122.423677 94.769551 82.123940
## [781] 84.384682 76.119913 204.411257 244.485784 174.506369
## [786] 194.475190 187.576824 219.241618 183.645520 170.911432
## [791] 198.236771 177.122156 181.564891 194.307478 187.107556
## [796] 6.942381 25.654823 188.575925 140.914886 35.323977
## [801] 23.914020 24.740560 22.954554 75.888428 62.552259
## [806] 79.731237 50.738832 58.155614 24.520786 118.459733
## [811] 85.529379 94.584042 93.003840 92.999789 92.828912
## [816] 52.191595 172.894451 175.328466 178.699841 124.259511
## [821] 114.206793 117.043094 111.501589 108.727169 152.644482
## [826] 15.884071 16.143270 19.414825 105.009557 108.874274
## [831] 108.892461 100.564082 102.871753 80.646317 29.016717
## [836] 21.088973 23.935007 172.100123 150.623739 147.942845
## [841] 152.257147 125.225080 123.689040 122.792585 140.344062
## [846] 133.274448 143.807146 127.831019 129.116781 138.529324
## [851] 142.159045 141.418952 95.717823 83.841033 104.851824
## [856] 98.020618 193.818136 235.971588 172.910544 192.153605
## [861] 184.243655 215.779715 177.703173 163.616639 190.963245
## [866] 169.562023 174.693966 186.247541 178.275056 18.737051
## [871] 184.535191 138.925018 39.216710 30.064439 31.620790
## [876] 29.801376 70.151597 56.595621 74.169502 50.567171
## [881] 57.179151 20.604436 112.768411 86.670382 96.366737
## [886] 95.519959 95.245282 95.084623 47.801433 168.708384
## [891] 171.418563 175.590062 117.739658 117.436853 120.536078
## [896] 114.368016 111.893482 147.355589 20.552740 20.723073
## [901] 23.940959 107.376679 111.290272 111.346714 102.504082
## [906] 104.749293 84.106386 32.092436 24.308347 26.988269
## [911] 169.147431 147.612011 145.172641 149.343494 120.858841
## [916] 120.175116 120.569480 134.381034 127.297535 137.532933
## [921] 121.572330 122.803384 132.500100 136.053707 135.273216
## [926] 94.604171 82.410214 98.304595 91.143963 196.670144
## [931] 238.185162 172.840403 192.342218 184.740028 216.357921
## [936] 179.021894 165.349018 192.729750 171.390538 176.307314
## [941] 188.262664 180.531009 176.192874 137.037872 53.955044
## [946] 48.185639 50.355542 48.525718 57.472319 43.474935
## [951] 62.067580 56.366583 60.478997 19.039807 99.532881
## [956] 93.984024 104.983203 105.841536 104.956089 104.821782
## [961] 41.580905 160.015183 163.559936 170.109685 101.285284
## [966] 129.071761 132.728396 125.214583 123.445490 135.244117
## [971] 36.207850 36.239004 38.998722 117.169036 121.141050
## [976] 121.285302 111.378079 113.438740 96.688492 45.996146
## [981] 39.207933 41.352716 164.178558 142.663354 140.961999
## [986] 144.666976 112.045807 114.055945 118.276990 119.992693
## [991] 112.900891 121.970751 106.145670 107.156985 117.879619
## [996] 121.132970 120.205821 95.955338 83.263654 81.831468
## [ reached getOption("max.print") -- omitted 2570 entries ]aquifer_pair$from## [1] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [19] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [37] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [55] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [73] 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2
## [91] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [109] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [127] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [145] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [163] 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3
## [181] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [199] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [217] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [235] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 4 4 4
## [253] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [271] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [289] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [307] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [325] 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 5 5 5
## [343] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
## [361] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
## [379] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
## [397] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 6 6 6 6
## [415] 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
## [433] 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
## [451] 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
## [469] 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
## [487] 6 6 6 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7
## [505] 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7
## [523] 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7
## [541] 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7
## [559] 7 7 7 7 7 7 7 7 7 8 8 8 8 8 8 8 8 8
## [577] 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8
## [595] 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8
## [613] 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8
## [631] 8 8 8 8 8 8 8 8 8 8 8 8 8 8 9 9 9 9
## [649] 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9
## [667] 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9
## [685] 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9
## [703] 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9
## [721] 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10
## [739] 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10
## [757] 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10
## [775] 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10
## [793] 10 10 10 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11
## [811] 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11
## [829] 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11
## [847] 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11
## [865] 11 11 11 11 11 12 12 12 12 12 12 12 12 12 12 12 12 12
## [883] 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12
## [901] 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12
## [919] 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12
## [937] 12 12 12 12 12 12 13 13 13 13 13 13 13 13 13 13 13 13
## [955] 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13
## [973] 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13
## [991] 13 13 13 13 13 13 13 13 13 13
## [ reached getOption("max.print") -- omitted 2570 entries ]aquifer_pair$lags## [1] 3 3 3 4 3 4 4 4 4 4 4 4 4 3 4 5 5 5
## [19] 2 2 2 3 3 4 1 4 4 4 4 4 2 3 3 4 2 5
## [37] 6 5 5 2 5 5 5 5 5 5 4 4 5 4 4 4 4 3
## [55] 3 3 1 2 3 2 2 3 2 2 2 2 2 3 3 2 3 7
## [73] 8 5 6 6 7 6 6 7 6 6 7 7 1 1 5 6 5 5
## [91] 5 5 5 5 5 4 1 4 5 5 5 4 4 4 3 3 6 4
## [109] 2 3 3 3 3 4 4 4 3 5 3 4 3 3 4 6 6 6
## [127] 3 3 3 3 2 4 4 5 5 3 2 2 2 3 2 1 5 5
## [145] 5 5 5 5 5 5 2 2 5 6 5 5 2 3 3 4 3 3
## [163] 4 3 3 4 4 1 4 5 4 4 4 4 4 4 4 4 2 4
## [181] 4 5 4 3 3 3 3 2 5 4 2 2 3 2 2 3 4 4
## [199] 4 5 3 3 3 3 4 5 5 5 3 3 3 2 2 3 4 4
## [217] 4 3 3 2 3 3 2 1 4 4 5 4 4 4 5 5 1 1
## [235] 4 5 5 6 3 4 4 5 4 4 4 4 4 4 4 5 5 5
## [253] 5 5 5 5 5 5 5 2 4 4 5 5 4 4 4 3 3 5
## [271] 4 2 2 2 2 2 4 4 4 4 5 3 3 3 3 5 5 5
## [289] 5 2 2 2 2 2 3 4 4 4 3 3 3 3 3 3 2 5
## [307] 5 5 5 5 5 5 5 1 2 5 6 4 6 3 3 3 4 3
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## [361] 4 5 5 5 5 5 2 2 2 5 5 5 5 5 4 2 2 2
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## [415] 2 2 1 7 6 3 3 3 3 2 2 2 3 3 2 4 4 5
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## [523] 5 2 2 2 4 5 5 4 4 4 2 2 2 6 5 5 6 4
## [541] 4 5 5 5 5 4 4 5 5 5 4 3 4 3 8 9 7 7
## [559] 7 8 7 6 7 7 7 7 7 1 1 1 1 1 7 6 2 1
## [577] 2 1 3 3 3 2 3 1 5 4 4 4 4 4 2 7 7 7
## [595] 5 5 5 5 5 6 1 1 1 4 5 5 4 4 3 2 1 1
## [613] 7 6 6 6 5 5 5 6 5 6 5 5 5 6 6 4 3 4
## [631] 4 8 9 7 8 7 8 7 7 8 7 7 7 7 1 1 1 1
## [649] 8 6 2 1 1 1 3 3 4 2 3 1 5 4 4 4 4 4
## [667] 3 7 7 7 5 5 5 5 5 6 1 1 1 4 5 5 4 4
## [685] 4 2 1 1 7 6 6 6 5 5 5 6 6 6 5 5 6 6
## [703] 6 4 4 4 4 8 9 7 8 7 9 7 7 8 7 7 7 7
## [721] 1 1 1 7 6 2 2 2 2 3 2 3 3 3 1 4 4 4
## [739] 4 4 4 2 6 7 7 4 5 5 5 5 6 2 2 2 5 5
## [757] 5 5 5 4 2 2 2 7 6 6 6 5 5 5 5 5 5 5
## [775] 5 5 5 5 4 4 4 3 8 10 7 8 7 9 7 7 8 7
## [793] 7 8 7 1 1 7 6 2 1 1 1 3 3 3 2 3 1 5
## [811] 4 4 4 4 4 2 7 7 7 5 5 5 5 5 6 1 1 1
## [829] 4 5 5 4 4 3 2 1 1 7 6 6 6 5 5 5 6 5
## [847] 6 5 5 6 6 6 4 4 4 4 8 9 7 8 7 8 7 7
## [865] 8 7 7 7 7 1 7 6 2 2 2 2 3 3 3 2 3 1
## [883] 5 4 4 4 4 4 2 7 7 7 5 5 5 5 5 6 1 1
## [901] 1 4 5 5 4 4 4 2 1 1 7 6 6 6 5 5 5 5
## [919] 5 6 5 5 5 6 5 4 4 4 4 8 9 7 8 7 8 7
## [937] 7 8 7 7 7 7 7 6 2 2 2 2 3 2 3 3 3 1
## [955] 4 4 4 4 4 4 2 6 7 7 4 5 5 5 5 5 2 2
## [973] 2 5 5 5 5 5 4 2 2 2 7 6 6 6 5 5 5 5
## [991] 5 5 4 4 5 5 5 4 4 4
## [ reached getOption("max.print") -- omitted 2570 entries ]
## Levels: 1 2 3 4 5 6 7 8 9 10aquifer_pair$to## [1] 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
## [19] 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37
## [37] 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55
## [55] 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73
## [73] 74 75 76 77 78 79 80 81 82 83 84 85 3 4 5 6 7 8
## [91] 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
## [109] 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44
## [127] 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62
## [145] 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80
## [163] 81 82 83 84 85 4 5 6 7 8 9 10 11 12 13 14 15 16
## [181] 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34
## [199] 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52
## [217] 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70
## [235] 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 5 6 7
## [253] 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
## [271] 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43
## [289] 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61
## [307] 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79
## [325] 80 81 82 83 84 85 6 7 8 9 10 11 12 13 14 15 16 17
## [343] 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35
## [361] 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53
## [379] 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71
## [397] 72 73 74 75 76 77 78 79 80 81 82 83 84 85 7 8 9 10
## [415] 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28
## [433] 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46
## [451] 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64
## [469] 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82
## [487] 83 84 85 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22
## [505] 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40
## [523] 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58
## [541] 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76
## [559] 77 78 79 80 81 82 83 84 85 9 10 11 12 13 14 15 16 17
## [577] 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35
## [595] 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53
## [613] 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71
## [631] 72 73 74 75 76 77 78 79 80 81 82 83 84 85 10 11 12 13
## [649] 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
## [667] 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49
## [685] 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67
## [703] 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85
## [721] 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28
## [739] 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46
## [757] 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64
## [775] 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82
## [793] 83 84 85 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
## [811] 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44
## [829] 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62
## [847] 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80
## [865] 81 82 83 84 85 13 14 15 16 17 18 19 20 21 22 23 24 25
## [883] 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43
## [901] 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61
## [919] 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79
## [937] 80 81 82 83 84 85 14 15 16 17 18 19 20 21 22 23 24 25
## [955] 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43
## [973] 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61
## [991] 62 63 64 65 66 67 68 69 70 71
## [ reached getOption("max.print") -- omitted 2570 entries ]aquifer.v<-est.variogram(aquifer_points,aquifer_pair,'resi')g4=ggplot(aquifer, aes(resi, Este)) +
geom_point() +
geom_line() +
xlab("Este") +
ylab("residuales2")
g5=ggplot(aquifer, aes(resi, Norte)) +
geom_point() +
geom_line() +
xlab("Norte") +
ylab("residuales2")
plot_grid(g4,g5)
aquifer_points=point(aquifer, x="Este", y="Norte")
fit.trend(aquifer_points,at="Profundidad", np=2, plot.it=TRUE)
## $beta
## x^0 y^0 x^1 y^0 x^2 y^0 x^0 y^1
## 2481.430108574 -8.373707821 0.001416675 -2.043419339
## x^1 y^1 x^0 y^2
## 0.026800556 -0.024643707
##
## $R
## x^0 y^0 x^1 y^0 x^2 y^0 x^0 y^1 x^1 y^1
## [1,] -9.219544 -155.6739 -41051.636 -731.67314 -16082.944
## [2,] 0.000000 595.1832 3500.219 57.75539 38829.771
## [3,] 0.000000 0.0000 39397.313 -117.36878 1909.315
## [4,] 0.000000 0.0000 0.000 485.98967 14332.040
## [5,] 0.000000 0.0000 0.000 0.00000 25401.055
## [6,] 0.000000 0.0000 0.000 0.00000 0.000
## x^0 y^2
## [1,] -85540.31
## [2,] 12491.66
## [3,] -23722.80
## [4,] 91118.22
## [5,] 3240.90
## [6,] 19989.20
##
## $np
## [1] 2
##
## $x
## [1] 42.78275 -27.39691 -1.16289 -18.61823 96.46549
## [6] 108.56243 88.36356 90.04213 93.17269 97.61099
## [11] 90.62946 92.55262 99.48996 -24.06744 -26.06285
## [16] 56.27842 73.03881 80.26679 80.23009 68.83845
## [21] 76.39921 64.46148 43.39657 39.07769 112.80450
## [26] 54.25899 6.13202 -3.80469 -2.23054 -2.36177
## [31] -2.18890 63.22428 -10.77860 -18.98889 -38.57884
## [36] 83.14496 -21.80248 -23.56457 -20.11299 -16.62654
## [41] 29.90748 100.91568 101.29544 103.26625 -14.31073
## [46] -18.13447 -18.12151 -9.88796 -12.16336 11.65754
## [51] 61.69122 69.57896 66.72205 -36.65446 -19.55102
## [56] -21.29791 -22.36166 21.14719 7.68461 -8.33227
## [61] 56.70724 59.00052 68.96893 70.90225 73.00243
## [66] 59.66237 61.87249 63.70810 5.62706 18.24739
## [71] 85.68824 105.07646 -101.64278 -145.23654 -73.99313
## [76] -94.48182 -88.84983 -120.25898 -86.02454 -72.79097
## [81] -100.17372 -78.83539 -83.69063 -95.61661 -87.55480
##
## $y
## [1] 127.62282 90.78732 84.89600 76.45199 64.58058
## [6] 82.92325 56.45348 39.25820 33.05852 56.27887
## [11] 35.08169 41.75238 59.15785 184.76636 114.07479
## [16] 26.84826 18.88140 12.61593 14.61795 107.77423
## [21] 95.99380 110.39641 53.61499 61.99805 45.54766
## [26] 147.81987 48.32772 40.40450 29.91113 33.82002
## [31] 33.68207 79.49924 175.11346 171.91695 158.52742
## [36] 159.11559 15.02551 9.41441 22.09269 17.25621
## [41] 175.12875 22.97808 22.96385 20.34239 31.26545
## [46] 30.18118 29.53241 38.14483 39.11081 18.73347
## [51] 32.94906 33.80841 33.93264 150.91457 137.78404
## [56] 131.82542 137.13680 139.26199 126.83751 107.77691
## [61] 171.26443 164.54863 177.24820 161.38136 162.98959
## [66] 170.10544 174.30177 173.91454 79.08730 77.39191
## [71] 139.81702 132.03181 10.65106 28.02333 87.97270
## [76] 86.62606 76.70991 80.76485 54.36334 43.09215
## [81] 42.89881 40.82141 46.50482 35.82183 29.39267
##
## $z
## [1] 1464 2553 2158 2455 1756 1702 1805 1797 1714 1466 1729
## [12] 1638 1736 1476 2200 1999 1680 1806 1682 1306 1722 1437
## [23] 1828 2118 1725 1606 2648 2560 2544 2386 2400 1757 1402
## [34] 1364 1735 1376 2729 2766 2736 2432 1024 1611 1548 1591
## [45] 2540 2352 2528 2575 2468 2646 1739 1674 1868 1865 1777
## [56] 1579 1771 1408 1527 2003 1386 1089 1384 1030 1092 1161
## [67] 1415 1231 2300 2238 1038 1332 3510 3490 2594 2650 2533
## [78] 3571 2811 2728 3136 2553 2798 2691 2946
##
## $residuals
## [1] -145.932017 296.391955 20.569629 155.586776
## [5] 136.944207 210.578982 112.643763 81.535500
## [9] 12.407325 -165.733666 11.643984 -55.843867
## [13] 123.038140 130.250727 132.838620 16.473072
## [17] -186.973641 -9.864104 -133.020821 -298.072286
## [21] 98.737035 -175.328351 -174.667016 118.113364
## [25] 176.632628 200.333264 366.232978 173.604750
## [29] 128.842139 -15.778284 -1.005758 -17.176812
## [33] -5.743382 -109.803640 35.578021 175.509274
## [37] 109.375693 113.827801 154.658230 -138.758151
## [41] -234.947039 -41.999962 -102.169175 -45.349545
## [45] 38.415648 -182.959426 -9.456222 134.544149
## [49] 14.873572 303.070200 -191.631118 -197.446346
## [53] -23.989926 92.632496 -47.092725 -308.538280
## [57] -72.511843 -213.402614 -260.643390 -17.741523
## [61] 187.380986 -159.999448 282.152142 -199.908135
## [65] -116.838018 -37.190026 262.093246 81.109636
## [69] 169.467368 176.796541 -289.932780 42.387375
## [73] 216.381585 -51.786437 30.159248 -53.946573
## [77] -219.188525 648.160187 -92.004756 -152.583829
## [81] 49.711612 -386.649271 -141.519561 -407.429504
## [85] -129.126052
##
## attr(,"class")
## [1] "trend.surface"g6=ggplot(aquifer.v, aes(resi, Norte)) +
geom_point() +
geom_line() +
xlab("Norte") +
ylab("residuales2")
g6=ggplot(aquifer.v, aes(bins, classic)) +
geom_point() +
geom_line() +
xlab("Rezago espacial, h") +
ylab("Estimador clásico del variograma")
g7=ggplot(aquifer.v, aes(bins, robust)) +
geom_point() +
geom_line() +
xlab("Rezago espacial, h") +
ylab("Estimador robusto 1 del variograma")
g8=ggplot(aquifer.v, aes(bins, med)) +
geom_point() +
geom_line() +
xlab("Rezago espacial, h") +
ylab("Estimador robusto 2 del variograma")
plot_grid(g6,g7,g8,nrow=1,ncol=3)
#par(mfrow=c(1,3))
print(aquifer.v)## lags bins classic robust med n
## 1 1 13.55308 43779.20 44355.34 47948.45 285
## 2 2 40.65923 71039.50 71176.29 73188.30 350
## 3 3 67.76539 80041.91 85367.59 93223.52 492
## 4 4 94.87154 67197.27 68067.40 73056.46 719
## 5 5 121.97770 73572.25 68052.99 66133.91 612
## 6 6 149.08385 57650.90 58608.95 58819.91 521
## 7 7 176.19001 65498.82 62167.57 68112.31 356
## 8 8 203.29616 130414.72 107613.55 77805.71 173
## 9 9 230.40231 161738.13 134102.60 123952.77 43
## 10 10 257.50847 35525.99 45217.14 58333.98 19plot(aquifer.v$robust)
plot(aquifer.v$med)
#points(aquifer.v$robust,col="red")
#points(aquifer.v$med,"blue")
aquifer.vmodExp<-fit.exponential(aquifer.v,c0=0,ce=40000,ae=20,plot.it=TRUE,iterations=30)## Initial parameter estimates: 0 40000 20
## Iteration: 1
## Gradient vector: -4432.441 977.0988 -8.943538
## New parameter estimates: 0.000001 40977.1 11.05646
##
## rse.dif = 3232643827 (rse = 3232643827 ) ; parm.dist = 977.1397
## Iteration: 2
## Gradient vector: -26700.7 22493.46 -2.800242
## New parameter estimates: 0.000001 63470.56 8.256219
##
## rse.dif = -17644208 (rse = 3214999619 ) ; parm.dist = 22493.46
## Iteration: 3
## Gradient vector: -11057.27 -15597.73 2.315183
## New parameter estimates: 0.000001 47872.83 10.5714
##
## rse.dif = -3772568 (rse = 3211227051 ) ; parm.dist = 15597.73
## Iteration: 4
## Gradient vector: -27525.12 16431.58 -1.824505
## New parameter estimates: 0.000001 64304.41 8.746897
##
## rse.dif = 3032851 (rse = 3214259902 ) ; parm.dist = 16431.58
## Iteration: 5
## Gradient vector: -20442.22 -7053.019 1.144197
## New parameter estimates: 0.000001 57251.39 9.891094
##
## rse.dif = -2468665 (rse = 3211791237 ) ; parm.dist = 7053.019
## Iteration: 6
## Gradient vector: -27557.41 7097.539 -0.7122805
## New parameter estimates: 0.000001 64348.93 9.178813
##
## rse.dif = 1486180 (rse = 3213277417 ) ; parm.dist = 7097.539
## Iteration: 7
## Gradient vector: -24787.06 -2758.919 0.3605893
## New parameter estimates: 0.000001 61590.01 9.539403
##
## rse.dif = -951749.7 (rse = 3212325667 ) ; parm.dist = 2758.919
## Iteration: 8
## Gradient vector: -26691.4 1898.737 -0.1885371
## New parameter estimates: 0.000001 63488.75 9.350866
##
## rse.dif = 471370.4 (rse = 3212797038 ) ; parm.dist = 1898.737
## Iteration: 9
## Gradient vector: -25850.35 -838.0686 0.09276125
## New parameter estimates: 0.000001 62650.68 9.443627
##
## rse.dif = -249219.6 (rse = 3212547818 ) ; parm.dist = 838.0686
## Iteration: 10
## Gradient vector: -26302.53 450.7265 -0.04631475
## New parameter estimates: 0.000001 63101.41 9.397312
##
## rse.dif = 121873.4 (rse = 3212669692 ) ; parm.dist = 450.7265
## Iteration: 11
## Gradient vector: -26086.54 -215.2624 0.02285916
## New parameter estimates: 0.000001 62886.14 9.420171
##
## rse.dif = -61031.79 (rse = 3212608660 ) ; parm.dist = 215.2624
## Iteration: 12
## Gradient vector: -26195.52 108.6221 -0.01133309
## New parameter estimates: 0.000001 62994.77 9.408838
##
## rse.dif = 30077.83 (rse = 3212638738 ) ; parm.dist = 108.6221
## Iteration: 13
## Gradient vector: -26142.08 -53.26613 0.005604603
## New parameter estimates: 0.000001 62941.5 9.414443
##
## rse.dif = -14922.96 (rse = 3212623815 ) ; parm.dist = 53.26613
## Iteration: 14
## Gradient vector: -26168.65 26.48517 -0.002774911
## New parameter estimates: 0.000001 62967.99 9.411668
##
## rse.dif = 7377.216 (rse = 3212631192 ) ; parm.dist = 26.48517
## Iteration: 15
## Gradient vector: -26155.53 -13.07801 0.001373075
## New parameter estimates: 0.000001 62954.91 9.413041
##
## rse.dif = -3653.216 (rse = 3212627539 ) ; parm.dist = 13.07801
## Iteration: 16
## Gradient vector: -26162.03 6.479831 -0.0006796194
## New parameter estimates: 0.000001 62961.39 9.412361
##
## rse.dif = 1807.514 (rse = 3212629346 ) ; parm.dist = 6.479831
## Iteration: 17
## Gradient vector: -26158.82 -3.20516 0.0003363367
## New parameter estimates: 0.000001 62958.18 9.412698
##
## rse.dif = -894.6895 (rse = 3212628451 ) ; parm.dist = 3.20516
## Iteration: 18
## Gradient vector: -26160.41 1.586717 -0.0001664615
## New parameter estimates: 0.000001 62959.77 9.412531
##
## rse.dif = 442.763 (rse = 3212628894 ) ; parm.dist = 1.586717
## Iteration: 19
## Gradient vector: -26159.62 -0.7851797 0.00008238305
## New parameter estimates: 0.000001 62958.98 9.412613
##
## rse.dif = -219.1369 (rse = 3212628675 ) ; parm.dist = 0.7851797
## Iteration: 20
## Gradient vector: -26160.01 0.3886224 -0.00004077272
## New parameter estimates: 0.000001 62959.37 9.412573
##
## rse.dif = 108.4519 (rse = 3212628784 ) ; parm.dist = 0.3886224
## Iteration: 21
## Gradient vector: -26159.82 -0.192328 0.00002017891
## New parameter estimates: 0.000001 62959.18 9.412593
##
## rse.dif = -53.67477 (rse = 3212628730 ) ; parm.dist = 0.192328
## Iteration: 22
## Gradient vector: -26159.91 0.09518727 -0.000009986825
## New parameter estimates: 0.000001 62959.28 9.412583
##
## rse.dif = 26.56425 (rse = 3212628756 ) ; parm.dist = 0.09518727
## Iteration: 23
## Gradient vector: -26159.86 -0.04710907 0.000004942611
## New parameter estimates: 0.000001 62959.23 9.412588
##
## rse.dif = -13.14703 (rse = 3212628743 ) ; parm.dist = 0.04710907
## Iteration: 24
## Gradient vector: -26159.89 0.02331501 -0.000002446166
## New parameter estimates: 0.000001 62959.25 9.412585
##
## rse.dif = 6.506637 (rse = 3212628750 ) ; parm.dist = 0.02331501
## Iteration: 25
## Gradient vector: -26159.88 -0.01153889 0.00000121064
## New parameter estimates: 0.000001 62959.24 9.412587
##
## rse.dif = -3.220223 (rse = 3212628747 ) ; parm.dist = 0.01153889
## Iteration: 26
## Gradient vector: -26159.88 0.005710766 -0.0000005991629
## New parameter estimates: 0.000001 62959.25 9.412586
##
## rse.dif = 1.593733 (rse = 3212628748 ) ; parm.dist = 0.005710766
## Iteration: 27
## Gradient vector: -26159.88 -0.002826337 0.0000002965342
## New parameter estimates: 0.000001 62959.24 9.412586
##
## rse.dif = -0.7887607 (rse = 3212628747 ) ; parm.dist = 0.002826337
## Iteration: 28
## Gradient vector: -26159.88 0.001398792 -0.0000001467587
## New parameter estimates: 0.000001 62959.24 9.412586
##
## rse.dif = 0.390368 (rse = 3212628748 ) ; parm.dist = 0.001398792
## Iteration: 29
## Gradient vector: -26159.88 -0.0006922786 0.00000007263263
## New parameter estimates: 0.000001 62959.24 9.412586
##
## rse.dif = -0.1931987 (rse = 3212628748 ) ; parm.dist = 0.0006922786
## Iteration: 30
## Gradient vector: -26159.88 0.0003426161 -0.00000003594667
## New parameter estimates: 0.000001 62959.24 9.412586
##
## rse.dif = 0.09561539 (rse = 3212628748 ) ; parm.dist = 0.0003426161
## Convergence not achieved!aquifer.vmodGau<-fit.gaussian(aquifer.v,c0=0,cg=50000,ag=50,plot.it=TRUE,iterations=30)## Initial parameter estimates: 0 50000 50
## Iteration: 1
## Gradient vector: 19162.34 -33401.14 -11.41191
## New parameter estimates: 19162.34 16598.86 38.58809
##
## rse.dif = 3299750048 (rse = 3299750048 ) ; parm.dist = 38507.55
## Iteration: 2
## Gradient vector: -1294.927 2010.017 -18.77473
## New parameter estimates: 17867.41 18608.87 19.81336
##
## rse.dif = -66430135 (rse = 3233319913 ) ; parm.dist = 2391.1
## Iteration: 3
## Gradient vector: 3201.043 -2835.169 9.216254
## New parameter estimates: 21068.46 15773.71 29.02961
##
## rse.dif = -24694350 (rse = 3208625564 ) ; parm.dist = 4276.09
## Iteration: 4
## Gradient vector: -4345.272 4292.413 -6.361973
## New parameter estimates: 16723.18 20066.12 22.66764
##
## rse.dif = 4004881 (rse = 3212630445 ) ; parm.dist = 6107.884
## Iteration: 5
## Gradient vector: 53.88685 -4.270081 2.074271
## New parameter estimates: 16777.07 20061.85 24.74191
##
## rse.dif = -3703977 (rse = 3208926468 ) ; parm.dist = 54.09555
## Iteration: 6
## Gradient vector: -391.4471 384.4526 -0.5571294
## New parameter estimates: 16385.62 20446.3 24.18478
##
## rse.dif = 588163 (rse = 3209514631 ) ; parm.dist = 548.6666
## Iteration: 7
## Gradient vector: 29.55911 -27.0943 0.07968918
## New parameter estimates: 16415.18 20419.21 24.26447
##
## rse.dif = -201438.9 (rse = 3209313192 ) ; parm.dist = 40.09799
## Iteration: 8
## Gradient vector: -6.581211 6.259206 -0.01207028
## New parameter estimates: 16408.6 20425.47 24.2524
##
## rse.dif = 26607.8 (rse = 3209339800 ) ; parm.dist = 9.082408
## Iteration: 9
## Gradient vector: 0.9423146 -0.8928955 0.001794561
## New parameter estimates: 16409.54 20424.57 24.25419
##
## rse.dif = -4077.43 (rse = 3209335722 ) ; parm.dist = 1.298161
## Iteration: 10
## Gradient vector: -0.1413215 0.1339887 -0.0002673761
## New parameter estimates: 16409.4 20424.71 24.25393
##
## rse.dif = 605.1536 (rse = 3209336327 ) ; parm.dist = 0.194743
## Iteration: 11
## Gradient vector: 0.02102884 -0.01993597 0.00003982407
## New parameter estimates: 16409.42 20424.69 24.25397
##
## rse.dif = -90.18701 (rse = 3209336237 ) ; parm.dist = 0.02897682
## Iteration: 12
## Gradient vector: -0.003132718 0.00296995 -0.000005931842
## New parameter estimates: 16409.42 20424.69 24.25396
##
## rse.dif = 13.43229 (rse = 3209336251 ) ; parm.dist = 0.004316777
## Iteration: 13
## Gradient vector: 0.0004666088 -0.0004423641 0.0000008835486
## New parameter estimates: 16409.42 20424.69 24.25396
##
## rse.dif = -2.000768 (rse = 3209336249 ) ; parm.dist = 0.0006429701
## Iteration: 14
## Gradient vector: -0.00006950174 0.00006589049 -0.0000001316048
## New parameter estimates: 16409.42 20424.69 24.25396
##
## rse.dif = 0.2980156 (rse = 3209336249 ) ; parm.dist = 0.00009577091
## Iteration: 15
## Gradient vector: 0.00001035231 -0.000009814415 0.00000001960261
## New parameter estimates: 16409.42 20424.69 24.25396
##
## rse.dif = -0.04438972 (rse = 3209336249 ) ; parm.dist = 0.00001426512
## Iteration: 16
## Gradient vector: -0.000001541989 0.000001461872 -0.000000002919836
## New parameter estimates: 16409.42 20424.69 24.25396
##
## rse.dif = 0.006611824 (rse = 3209336249 ) ; parm.dist = 0.000002124808
## Iteration: 17
## Gradient vector: 0.000000229702 -0.0000002177649 0.0000000004349504
## New parameter estimates: 16409.42 20424.69 24.25396
##
## rse.dif = -0.0009841919 (rse = 3209336249 ) ; parm.dist = 0.0000003165203
## Iteration: 18
## Gradient vector: -0.0000000342286 0.00000003244849 -0.00000000006480716
## New parameter estimates: 16409.42 20424.69 24.25396
##
## rse.dif = 0.0001459122 (rse = 3209336249 ) ; parm.dist = 0.00000004716456
## Iteration: 19
## Gradient vector: 0.000000005117361 -0.000000004848551 0.000000000009688533
## New parameter estimates: 16409.42 20424.69 24.25396
##
## rse.dif = -0.00002241135 (rse = 3209336249 ) ; parm.dist = 0.000000007051061
## Iteration: 20
## Gradient vector: -0.0000000007696674 0.0000000007270391 -0.000000000001463951
## New parameter estimates: 16409.42 20424.69 24.25396
##
## rse.dif = 0.000004291534 (rse = 3209336249 ) ; parm.dist = 0.000000001060296
## Iteration: 21
## Gradient vector: 0.0000000001036345 -0.00000000009511823 0.0000000000002010728
## New parameter estimates: 16409.42 20424.69 24.25396
##
## rse.dif = -0.000001430511 (rse = 3209336249 ) ; parm.dist = 0.0000000001390071
## Iteration: 22
## Gradient vector: -0.00000000001632815 0.00000000001786392 -0.00000000000003703972
## New parameter estimates: 16409.42 20424.69 24.25396
##
## rse.dif = 0.000001430511 (rse = 3209336249 ) ; parm.dist = 0.00000000002329446
## Iteration: 23
## Gradient vector: -0.000000000003827252 0.000000000002836377 0.000000000000003527592
## New parameter estimates: 16409.42 20424.69 24.25396
##
## rse.dif = 0 (rse = 3209336249 ) ; parm.dist = 0.00000000000514488
##
## Convergence achieved by sums of squares.
## Final parameter estimates: 16409.42 20424.69 24.25396aquifer.vmodWave<-fit.wave(aquifer.v,c0=0,cw=40000,aw=10,plot.it=TRUE,iterations=30,weighted=T)## Initial parameter estimates: 0 40000 10
## Iteration: 1
## Gradient vector: 18650.32 -21981.27 -0.7942028
## New parameter estimates: 18650.32 18018.73 9.205797
##
## rse.dif = 3409704989 (rse = 3409704989 ) ; parm.dist = 28827.26
## Iteration: 2
## Gradient vector: 812.9227 -1109.399 -1.187299
## New parameter estimates: 19463.25 16909.33 8.018498
##
## rse.dif = -289093760 (rse = 3120611230 ) ; parm.dist = 1375.358
## Iteration: 3
## Gradient vector: -6990.158 6973.566 0.9858099
## New parameter estimates: 12473.09 23882.9 9.004308
##
## rse.dif = 24044562 (rse = 3144655792 ) ; parm.dist = 9873.851
## Iteration: 4
## Gradient vector: 7025.438 -6960.473 -1.260353
## New parameter estimates: 19498.53 16922.43 7.743955
##
## rse.dif = -56767551 (rse = 3087888241 ) ; parm.dist = 9889.639
## Iteration: 5
## Gradient vector: -9210.154 9213.61 1.066674
## New parameter estimates: 10288.37 26136.04 8.810629
##
## rse.dif = 175986924 (rse = 3263875165 ) ; parm.dist = 13027.57
## Iteration: 6
## Gradient vector: 11994.7 -11983.26 -2.255679
## New parameter estimates: 22283.07 14152.77 6.55495
##
## rse.dif = -196728543 (rse = 3067146622 ) ; parm.dist = 16954.98
## Iteration: 7
## Gradient vector: -14060.45 14195.04 -1.578095
## New parameter estimates: 8222.625 28347.81 4.976855
##
## rse.dif = 147278852 (rse = 3214425474 ) ; parm.dist = 19979.87
## Iteration: 8
## Gradient vector: -15826.64 16212.91 0.3854677
## New parameter estimates: 0.000001 44560.72 5.362323
##
## rse.dif = -46983778 (rse = 3167441696 ) ; parm.dist = 18178.84
## Iteration: 9
## Gradient vector: 13145.08 -21444.98 -0.8756698
## New parameter estimates: 13145.08 23115.75 4.486653
##
## rse.dif = -757940879 (rse = 2409500817 ) ; parm.dist = 25153.13
## Iteration: 10
## Gradient vector: -9434763 9682459 25.73116
## New parameter estimates: 0.000001 9705575 30.21781
##
## rse.dif = 1636307005 (rse = 4045807822 ) ; parm.dist = 9682468
## Iteration: 11
## Gradient vector: 20962.2 -9688482 0.02156687
## New parameter estimates: 20962.2 17093.21 30.23938
##
## rse.dif = 83628062 (rse = 4129435883 ) ; parm.dist = 9688504
## Iteration: 12
## Gradient vector: 7173.136 -8587.116 1.22582
## New parameter estimates: 28135.34 8506.099 31.4652
##
## rse.dif = -628497356 (rse = 3500938527 ) ; parm.dist = 11188.94
## Iteration: 13
## Gradient vector: 2974.651 -2890.861 -4.19572
## New parameter estimates: 31109.99 5615.237 27.26947
##
## rse.dif = -192443200 (rse = 3308495327 ) ; parm.dist = 4147.969
## Iteration: 14
## Gradient vector: -2399.351 1443.698 15.69929
## New parameter estimates: 28710.64 7058.936 42.96876
##
## rse.dif = 147479203 (rse = 3455974530 ) ; parm.dist = 2800.25
## Iteration: 15
## Gradient vector: 4786.661 2165.107 -43.14322
## New parameter estimates: 33497.3 9224.042 0.000001
##
## rse.dif = -686128323 (rse = 2769846206 ) ; parm.dist = 5253.728
## Iteration: 16
## Gradient vector: -7188.309 -0.0000005926894 0
## New parameter estimates: 26308.99 9224.042 0.000001
##
## rse.dif = 686457465 (rse = 3456303671 ) ; parm.dist = 7188.309
## Iteration: 17
## Gradient vector: -0.000005339325 -0.0000005926894 0
## New parameter estimates: 26308.99 9224.042 0.000001
##
## rse.dif = 0.4889326 (rse = 3456303672 ) ; parm.dist = 0.000005372118
## Iteration: 18
## Gradient vector: 0.0000005926854 -0.0000005926894 0
## New parameter estimates: 26308.99 9224.042 0.000001
##
## rse.dif = 0.000002384186 (rse = 3456303672 ) ; parm.dist = 0.0000008381857
## Iteration: 19
## Gradient vector: 0.0000005926902 -0.0000005926894 0
## New parameter estimates: 26308.99 9224.042 0.000001
##
## rse.dif = -0.000001907349 (rse = 3456303672 ) ; parm.dist = 0.0000008381882
## Iteration: 20
## Gradient vector: 0.0000005926902 -0.0000005926894 0
## New parameter estimates: 26308.99 9224.042 0.000001
##
## rse.dif = 0 (rse = 3456303672 ) ; parm.dist = 0.0000008381882
##
## Convergence achieved by sums of squares.
## Final parameter estimates: 26308.99 9224.042 0.000001curve(65000*(1-(14/x)*sin(x/14)),0,300,ylim=c(0,200000))
points(aquifer.v$bins,aquifer.v$classic,col=3)
text(aquifer.v$bins,aquifer.v$classic,aquifer.v$n,col=2)
curve(200000*(1-exp(-x/170)),0,300)
points(aquifer.v$bins,aquifer.v$classic,col=2)
curve(65000*(1-(14/x)*sin(x/14)),0,300,ylim=c(0,200000))
points(aquifer.v$bins,aquifer.v$classic,col=3)
text(aquifer.v$bins,aquifer.v$classic,aquifer.v$n,col=2)
aquifer.vmodExp<-fit.exponential(aquifer.v,c0=0,ce=200000,ae=170,plot.it=TRUE,iterations=30,weighted=T)## Initial parameter estimates: 0 200000 170
## Iteration: 1
## Gradient vector: 16365.66 -238859.4 -103.7436
## New parameter estimates: 16365.66 0.000001 66.25643
##
## rse.dif = 3826411368 (rse = 3826411368 ) ; parm.dist = 200668.5
## Iteration: 2
## Gradient vector: 7737.246 16547.95 166070861252
## New parameter estimates: 24102.91 16547.95 166070861318
##
## rse.dif = -767474321 (rse = 3058937047 ) ; parm.dist = 166070861252
## Iteration: 3
## Gradient vector: 3355.03 12424786768746 0
## New parameter estimates: 27457.94 12424786785294 166070861318
##
## rse.dif = -120011141 (rse = 2938925906 ) ; parm.dist = 12424786768746
## Iteration: 4
## Gradient vector: 423.3165 -663474885968 0
## New parameter estimates: 27881.25 11761311899326 166070861318
##
## rse.dif = 11801483 (rse = 2950727388 ) ; parm.dist = 663474885968
## Iteration: 5
## Gradient vector: 3.873181 -6320523090 0
## New parameter estimates: 27885.12 11754991376237 166070861318
##
## rse.dif = 128956.4 (rse = 2950856345 ) ; parm.dist = 6320523090
## Iteration: 6
## Gradient vector: 0.02266712 -36921321 0
## New parameter estimates: 27885.15 11754954454916 166070861318
##
## rse.dif = 752.3639 (rse = 2950857097 ) ; parm.dist = 36921321
## Iteration: 7
## Gradient vector: 0.0001316946 -214507.3 0
## New parameter estimates: 27885.15 11754954240408 166070861318
##
## rse.dif = 4.371067 (rse = 2950857102 ) ; parm.dist = 214507.3
## Iteration: 8
## Gradient vector: 0.0000007651061 -1246.218 0
## New parameter estimates: 27885.15 11754954239162 166070861318
##
## rse.dif = 0.02539396 (rse = 2950857102 ) ; parm.dist = 1246.217
## Iteration: 9
## Gradient vector: 0.000000004444639 -7.24441 0
## New parameter estimates: 27885.15 11754954239155 166070861318
##
## rse.dif = 0.0001482964 (rse = 2950857102 ) ; parm.dist = 7.244141
## Iteration: 10
## Gradient vector: 0.00000000002418472 -0.03727549 0
## New parameter estimates: 27885.15 11754954239155 166070861318
##
## rse.dif = 0.0000009536743 (rse = 2950857102 ) ; parm.dist = 0.03710938
##
## Convergence achieved by sums of squares.
## Final parameter estimates: 27885.15 11754954239155 166070861318aquifer.vmodwave<-fit.wave(aquifer.v,c0=4000,cw=30000,aw=15,plot.it=TRUE,iterations=0,weighted=T)
## Convergence not achieved!aquifer.vmodExp_0<-fit.exponential(aquifer.v,c0=0,ce=200000,ae=170,plot.it=TRUE,iterations=0,weighted=T)
## Convergence not achieved!aquifer.vmodwave_0<-fit.wave(aquifer.v,c0=4000,cw=30000,aw=15,plot.it=TRUE,iterations=0,weighted=T)
## Convergence not achieved!aquifer.spherical<-fit.spherical(aquifer.v,c0=0,cs=35000,as=70,plot.it=TRUE,iterations=0,weighted=T)
## Convergence not achieved!ggplot(aquifer.v, aes(bins, classic)) +
geom_point() +
geom_line() +
xlab("Rezago espacial, h") +
ylab("Estimador clásico del variograma")+
xlim(0, 300) +
geom_function(aes(color = "Exponencial"),
fun =~4000+150000*(1-exp(-.x/100))
) +
geom_function(aes(color = "Seno cardinal"),
fun =~4000+30000*(1-((15/.x)*sin(.x/15)))
) + xlab("Rezago espacial") + ylab("Modelos teóricos de semivariogramas") 
Kriging_aquifer <- point(data.frame(list(x=10,y=80)))
Kriging_aquifer <- krige(Kriging_aquifer, aquifer_points, 'resi', aquifer.vmodExp_0)##
## Using all points.
## Preparing the kriging system matrix...
## Inverting the matrix...
## Predicting.Kriging_aquifer##
## Point object: x
##
## Locations: 1
##
## Attributes:
## x
## y
## do
## zhat
## sigma2hatKriging_aquifer$sigma2hat## [1] 7010.452Kriging_aquifer <- point(data.frame(list(x=10,y=80)))
Kriging_aquifer <- krige(Kriging_aquifer, aquifer_points, 'resi', aquifer.vmodwave_0)##
## Using all points.
## Preparing the kriging system matrix...
## Inverting the matrix...
## Predicting.Kriging_aquifer##
## Point object: x
##
## Locations: 1
##
## Attributes:
## x
## y
## do
## zhat
## sigma2hatKriging_aquifer$zhat## [1] 196.2781Kriging_aquifer$sigma2hat## [1] 5169.927grid <- list(x=seq(min(aquifer$Este),max(aquifer$Este),by=20),y=seq(min(aquifer$Norte),max(aquifer$Norte),by=10))
grid$xr <- range(grid$x)
grid$xs <- grid$xr[2] - grid$xr[1]
grid$yr <- range(grid$y)
grid$ys <- grid$yr[2] - grid$yr[1]
grid$max <- max(grid$xs, grid$ys)
grid$xy <- data.frame(cbind(c(matrix(grid$x, length(grid$x), length(grid$y))),
c(matrix(grid$y, length(grid$x), length(grid$y), byrow=TRUE))))
colnames(grid$xy) <- c("x", "y")
grid$point <- point(grid$xy)
grid$krige <- krige(grid$point,aquifer_points,'resi',aquifer.vmodwave_0,maxdist=180,extrap=FALSE)##
## Using points within 180 units of prediction points.
## Predicting..........................................................................................................................................................................................................................................op <- par(no.readonly = TRUE)
par(pty="s")
plot(grid$xy, type="n", xlim=c(grid$xr[1], grid$xr[1]+grid$max),ylim=c(grid$yr[1], grid$yr[1]+grid$max))
image(grid$x,grid$y,matrix(grid$krige$zhat,length(grid$x),length(grid$y)),add=TRUE)
contour(grid$x,grid$y,matrix(grid$krige$zhat,length(grid$x),length(grid$y)),add=TRUE)
x11()
op <- par(no.readonly = TRUE)
par(pty="s")
plot(grid$xy, type="n", xlim=c(grid$xr[1], grid$xr[1]+grid$max),ylim=c(grid$yr[1], grid$yr[1]+grid$max))
image(grid$x,grid$y,matrix(grid$krige$sigma2hat,length(grid$x),length(grid$y)), add=TRUE)
contour(grid$x,grid$y,matrix(grid$krige$sigma2hat,length(grid$x),length(grid$y)),add=TRUE)
9 Cokriging
9.1 Librerías
library(sp)
library(gstat)
library(sf)
library(rgdal)
library(ggplot2)
library(plotly)
library(Matrix)9.2 Descripción de los datos
Cokriging para las variables \(NO2\), \(O3\), y \(NOX\). La variable de principal riesgo es ozono (\(O3\)), así que se usan las otras dos como covariables espaciales. Día 2020/01/16 A las 17 horas.
datos <- read.csv("2_COK_G_stat/Air_polution_cdmx_2020_01_16_17h.csv")
datos <- datos[c("Estacion",
"X",
"Y",
"NO2",
"O3",
"NOX")]
pander::pander((datos))| Estacion | X | Y | NO2 | O3 | NOX |
|---|---|---|---|---|---|
| AJU | 482901 | 2117907 | NA | 50 | NA |
| AJM | 478188 | 2130946 | 5 | 51 | 8 |
| ATI | 473346 | 2164689 | 20 | 70 | 20 |
| CAM | 482180 | 2152665 | 23 | 83 | 24 |
| CCA | 481502 | 2136931 | 6 | 46 | 8 |
| CUA | 469366 | 2141275 | 9 | 56 | 10 |
| CUT | 479189 | 2180751 | 13 | 75 | 14 |
| FAC | 474444 | 2154232 | 31 | 71 | 35 |
| HGM | 484020 | 2146380 | 25 | 81 | 31 |
| IZT | 487647 | 2143367 | 21 | 61 | 23 |
| LLA | 495842 | 2164872 | 14 | 81 | 15 |
| LPR | 487650 | 2160000 | NA | 64 | NA |
| MER | 487445 | 2147815 | 23 | 79 | 26 |
| MGH | 478716 | 2145543 | NA | 66 | NA |
| MON | 510196 | 2151776 | 9 | 80 | 10 |
| MPA | 498809 | 2123036 | 1 | 50 | NA |
| NEZ | 497038 | 2144394 | 8 | 62 | 9 |
| PED | 478557 | 2136817 | 6 | 56 | 6 |
| SAG | 496819 | 2159801 | 16 | 80 | 16 |
| SFE | 472393 | 2140390 | 9 | 66 | 10 |
| TAH | 498890 | 2128098 | 3 | 47 | 3 |
| TLA | 478535 | 2159383 | 26 | 64 | 30 |
| TLI | 481421 | 2167509 | 18 | 86 | 20 |
| UAX | 489113 | 2134517 | NA | 54 | NA |
| UIZ | 492241 | 2140751 | 7 | 45 | 7 |
| VIF | 489875 | 2173664 | 19 | 80 | 22 |
| XAL | 491355 | 2159031 | 27 | 80 | 27 |
9.3 Matrices de coregionalización.
9.3.1 Matriz definida positiva para el modelo Esférico.
mat1 <- cbind(c(30, 30, 30),
c(30, 50, 30),
c(30, 30, 35))
#matriz definida positiva "cercana"
mat1 <- data.frame(as.matrix(nearPD(mat1)$mat))
names(mat1) <- c("NO2", "O3", "NOX")
row.names(mat1) <- c("NO2", "O3", "NOX")
pander::pander(mat1)| NO2 | O3 | NOX | |
|---|---|---|---|
| NO2 | 30 | 30 | 30 |
| O3 | 30 | 50 | 30 |
| NOX | 30 | 30 | 35 |
9.3.2 Matriz definida positiva para el modelo efecto Hueco.
mat2 <- cbind(c(13.02, 24.5, 18.739),
c(24.58, 46.4, 35.36),
c(18.73, 35.36, 26.95))
mat2 <- data.frame(as.matrix(nearPD(mat2)$mat))
names(mat2) <- c("NO2", "O3", "NOX")
row.names(mat2) <- c("NO2", "O3", "NOX")
pander::pander(mat2)| NO2 | O3 | NOX | |
|---|---|---|---|
| NO2 | 13.02 | 24.54 | 18.73 |
| O3 | 24.54 | 46.4 | 35.36 |
| NOX | 18.73 | 35.36 | 26.96 |
9.4 Definición de objeto en gstat
9.4.1 Semivariogramas univariados
vgmno2 <- vgm(psill = mat1[1, 1],
model = "Sph",
range = 6096,
add.to = vgm(psill = mat2[1, 1],
model = "Hol",
range = 2294))
vgmo3 <- vgm(psill = mat1[2, 2],
model = "Sph",
range = 6096,
add.to = vgm(psill = mat2[2, 2],
model = "Hol",
range = 2294))
vgmnox <- vgm(psill = mat1[3, 3],
model = "Sph",
range = 6096,
add.to = vgm(psill = mat2[3, 3],
model = "Hol",
range = 2294))9.4.2 Semivarogramas cruzados (Bivariados)
vgmno2_o3 <- vgm(psill = mat1[1, 2], model = "Sph",
range = 6096,
add.to = vgm(psill = mat2[1, 2],
model = "Hol",
range = 2294))
vgmno2_nox <- vgm(psill = mat1[1, 3],
model = "Sph",
range = 6096,
add.to = vgm(psill = mat2[1, 3],
model = "Hol",
range = 2294))
vgmno3_nox <- vgm(psill = mat1[2, 3],
model = "Sph",
range = 6096,
add.to = vgm(psill = mat2[2, 3],
model = "Hol",
range = 2294))9.4.3 gstat
remove_na <- function(frame, vari_) {
# Remove na from sp object
datos1 <- frame
bool <- !is.na(datos1@data[vari_])
datos1@data <- datos1@data[bool, ]
datos1@coords <- datos1@coords[bool, ]
return(datos1)
}
coordinates(datos) <- ~ X + Y
g_st <- gstat(NULL,
id = "NO2",
formula = NO2 ~ X + Y,
model = vgmno2,
data = remove_na(datos, "NO2"))
g_st <- gstat(g_st,
id = "O3",
formula = O3 ~ Y,
model = vgmo3,
data = remove_na(datos, "O3"))
g_st <- gstat(g_st,
id = "NOX",
formula = NOX ~ Y,
model = vgmnox,
data = remove_na(datos, "NOX"))
#Cruzados
g_st <- gstat(g_st,
id = c("NO2", "O3"),
model = vgmno2_o3)
g_st <- gstat(g_st,
id = c("NO2", "NOX"),
model = vgmno2_nox)
g_st <- gstat(g_st,
id = c("O3", "NOX"),
model = vgmno3_nox)
pander::pander(do.call(rbind, g_st$model)[, 1:3])| model | psill | range | |
|---|---|---|---|
| NO2.1 | Hol | 13.02 | 2294 |
| NO2.2 | Sph | 30 | 6096 |
| O3.1 | Hol | 46.4 | 2294 |
| O3.2 | Sph | 50 | 6096 |
| NOX.1 | Hol | 26.96 | 2294 |
| NOX.2 | Sph | 35 | 6096 |
| NO2.O3.1 | Hol | 24.54 | 2294 |
| NO2.O3.2 | Sph | 30 | 6096 |
| NO2.NOX.1 | Hol | 18.73 | 2294 |
| NO2.NOX.2 | Sph | 30 | 6096 |
| O3.NOX.1 | Hol | 35.36 | 2294 |
| O3.NOX.2 | Sph | 30 | 6096 |
9.4.4 Estimación del semivariograma
plot(variogram(g_st),
model = g_st$model,
pl = T,
xlab = "Distancias",
ylab = "Semivarianza")
9.4.5 Mapas de predicción de O3 con las covariables espaciales NO2 y NOX
prediction_plot <- function(g_object, variable, map_path) {
map <- readOGR(map_path)
new <- sp::spsample(map, n = 100000, type = "regular")
coordinates(new) ~ x1 + x2
colnames(new@coords) <- c("X", "Y")
predic <- predict(g_object, newdata = new)
prediction <- data.frame(predic)
pred <- paste(variable, ".pred", sep = "")
plot <- ggplot(prediction, aes_string("X", "Y", fill = pred)) +
geom_tile() +
scale_fill_viridis_c() +
theme_void()
return(plot)
}
variance_plot <- function(g_object, variable, map_path) {
map <- readOGR(map_path)
new <- sp::spsample(map, n = 10000, type = "regular")
coordinates(new) ~ x1 + x2
colnames(new@coords) <- c("X", "Y")
predic <- predict(g_object, newdata = new)
prediction <- data.frame(predic)
var <- paste(variable, ".var", sep = "")
plot <- ggplot(prediction, aes_string("X", "Y", fill = var)) +
geom_tile() +
scale_fill_viridis_c(option = "inferno",
direction = -1) +
theme_void()
return(plot)
}
cv_plot <- function(g_object, variable, map_path) {
map <- readOGR(map_path)
new <- sp::spsample(map, n = 10000, type = "regular")
coordinates(new) ~ x1 + x2
colnames(new@coords) <- c("X", "Y")
predic <- predict(g_object, newdata = new)
prediction <- data.frame(predic)
pred <- paste(variable, ".pred", sep = "")
var <- paste(variable, ".var", sep = "")
aux <- abs(sqrt(prediction[var]) / abs(prediction[pred]))
aux[aux > 1] <- 1
prediction["cv"] <- aux
plot <- ggplot(prediction, aes_string("X", "Y", fill = "cv")) +
geom_tile() +
scale_fill_viridis_c(option = "magma",
direction = -1) +
theme_void()
return(plot)
}
pl1 <- prediction_plot(g_st, "O3",
"2_COK_G_stat/SP/mpiosutm.shp")## OGR data source with driver: ESRI Shapefile
## Source: "/home/martha/Documentos/Cursos EE UN/2_COK_G_stat/SP/mpiosutm.shp", layer: "mpiosutm"
## with 54 features
## It has 7 fields
## Linear Model of Coregionalization found. Good.
## [using universal cokriging]pl2 <- variance_plot(g_st, "O3",
"2_COK_G_stat/SP/mpiosutm.shp")## OGR data source with driver: ESRI Shapefile
## Source: "/home/martha/Documentos/Cursos EE UN/2_COK_G_stat/SP/mpiosutm.shp", layer: "mpiosutm"
## with 54 features
## It has 7 fields
## Linear Model of Coregionalization found. Good.
## [using universal cokriging]pl3 <- cv_plot(g_st, "O3",
"2_COK_G_stat/SP/mpiosutm.shp")## OGR data source with driver: ESRI Shapefile
## Source: "/home/martha/Documentos/Cursos EE UN/2_COK_G_stat/SP/mpiosutm.shp", layer: "mpiosutm"
## with 54 features
## It has 7 fields
## Linear Model of Coregionalization found. Good.
## [using universal cokriging]ggplotly(pl1)